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Contents
1 Number Theory
1
2 HCF and LCM
9
3 Ages
13
4 Average
17
5 Alligation and Mixture
19
6 Boats and Streams
21
7 Calender
23
8 Clock
25
9 Mensuration
29
10 Permutation
31
11 Percentage
33
12 Partnership
37
13 Probability
39
14 Profit, Loss and Discount
43
15 Sequences and Series
47
16 Ratio and Proportion
49
17 Real Number System
51
3
18
Simplifications
Department
of Extension and Career Guidance
53
19 Speed Calculations
57
20 Time and work
59
21 Time, Speed & Distance
63
22 Average
67
23 Bank Discount
69
24 True Discount
71
25 Website Model Question Papers Collection
73
Department of Extension and Career Guidance
4
Chapter 1
Number Theory
Important Facts and Formulas
1. Natural numbers: These are the numbers (1,2,3,etc.) that are used for counting. In other words, all
positive integers are natural numbers.
There are infinite natural numbers and the number 1 is the least number.
Examples of natural numbers 1,2,4,8,4321 and so on.
The following numbers are examples of numbers that are not natural: -2, -31, 2.38, 0 and so on.
Based on divisiblity, there could be two types of natural numbers: Prime and Composite.
2. Prime Numbers: A natural number larger than unity is a prime number if it dies not have other divisors
except for itself and unity.
Note: Unity (i.e. 1) is not a prime number.
Some properties of Prime numbers:
• The lowest prime number is 2.
• 2 is also the only even prime number.
• The lowest odd prime number is 3.
To check whether a number N is prime, adopt the following process:
(a) Take the square root of the number.
(b) Round of the square root to the immediately lower integer. Call this number z. For example if you have
to check for 181, its square root will be 13. Hence, the value of z, in this case will be 13.
(c) Check for divisiblity of the number N by all prime numbers below z. If there is no prime number below
the value of z which divides N then the number will be prime.
Example: Check 239 is prime or not.
√
(a) The value of 239 ;ies between 15 to 16. Hence, take the value of z as 16.
(b) Prime numbers less than 16 are 2,3,5,7,11 and 13.
(c) 239 is not divisible by any of these.
(d) Hence 239 is a prime number.
3. Exponents and Powers:
(a) Very large numbers are difficult to read, understand, compare and operate upon. To make all these
easier, we use exponents, converting many of the large numbers in a shorter form.
1
Department of Extension and Career Guidance
CHAPTER 1. NUMBER THEORY
(b) The following are exponential forms of some numbers:
i. 10, 000 = 104 (read as 10 raised to 4)
ii. 243 = 35
iii. 128 = 27
Here, 10, 3 and 2 are the bases, whereas 4, 5 and 7 are their respective exponents. We also say, 10,000
is the 4th power of 10, 243 is the 5th power of 3, etc.
(c) Numbers in exponential form obey certain laws, which are:
For any non-zero integers a and b and whole numbers m and n,
am × an = am+n
am ÷ an = am−n , m > n.
(am )n = amn
am × bm = (ab)m
m
am ÷ bm = ab
a0 = 1
(−1)even number = 1
viii. (−1)odd number = −1.
i.
ii.
iii.
iv.
v.
vi.
vii.
SQUARE up to 50
N2
1
4
9
16
25
36
49
64
81
100
N
1
2
3
4
5
6
7
8
9
10
N2
121
144
169
196
225
256
289
324
361
400
N
11
12
13
14
15
16
17
18
19
20
N
21
22
23
24
25
26
27
28
29
30
N2
441
484
529
576
625
676
729
784
841
900
N
31
32
33
34
35
36
37
38
39
40
N2
961
1024
1089
1156
1225
1296
1369
1444
1521
1600
N
41
42
43
44
45
46
47
48
49
50
N
21
22
23
24
25
N3
9261
10648
12167
13824
15626
N2
1681
1764
1849
1936
2025
2116
2209
2304
2401
2500
CUPE up to 30
N
1
2
3
4
5
N3
1
8
27
64
125
N
6
7
8
9
10
N3
216
343
512
729
1000
N
11
12
13
14
15
N3
1331
1728
2197
2744
3375
N
16
17
18
19
20
N3
4096
4913
5832
6859
8000
N
26
27
28
29
30
N3
17576
19683
21952
24389
27000
Solved Examples
1. Simplify:
(a) 272/3 = (33 )2/3 = 33×2/3 = 32 = 9.
1
.
256
= (2/5)3×−4/3 = (2/5)−4 = (5/2)4 = 625/16.
(b) 1024−4/5 = (210 )−4/5 = 210×−4/5 = 2−8 =
(c) (8/125)−4/3 = {(2/5)3 }−4/3
2. Evaluate:
(a) (0.00032)3/5 = (32/100000)3/5 = {(2/10)5 }3/5 = (1/5)5×3/5 = (1/5)3 = 1/125.
(b) (256)0.16 × (16)0.18 = (162 )0.16 × (16)0.18 = (16)0.32 × (16)0.18 = 160.32+0.18 = 160.5 = 161/2 = 4.
Department of Extension and Career Guidance
2
Department of Extension and Career Guidance
3. What is the quotient when (x−1 − 1) is divisible by (x − 1)?
Solution:
1−x
1
x−1 − 1
1−x
1
−1
x
x −1
=
=
=
×
=
.
x−1
x−1
x−1
x
x−1
x
4. If x−1 + 2x+1 = 1280, then find the value of x.
Solution:
exercises
1. 4003 × 77 − 21045 =? × 116
(a) 2477
4. Look at this series: 7, 10, 8, 11, 9, 12, ... What
number should come next?
(a)
(b)
(c)
(d)
(b) 2478
(c) 2467
(d) 2476
7
10
12
13
(e) None of these
5. Look at this series: 36, 34, 30, 28, 24, ... What
number should come next?
Answer: (e)
Explanation:
? × 116
=
4003 × 77 − 21045
? × 116 = 308281 − 21045
? = 287186/17
?
=
16893.2.
Short Cut:
First Check unit digit of LHS. i.e. = 6.
Now check the unit digit of ?. We need unit digit
of ? is 1 or 6.
√
√
2. 33124 × 2601 − 832 =?2 + 372
(a)
(b)
(c)
(d)
20
22
23
26
6. Look at this series: 22, 21, 23, 22, 24, 23, ... What
number should come next?
(a)
(b)
(c)
(d)
22
24
25
26
7. Look at this series: 53, 53, 40, 40, 27, 27, ... What
number should come next?
(a) 37
(b) 33
(a)
(b)
(c)
(d)
(c) 34
(d) 28
(e) None of these
Answer: (e)
Explanation:
8. Look at this series: 21, 9, 21, 11, 21, 13, 21, ...
What number should come next?
?2 + 372
2
? + 1369
√
√
33124 × 2601 − 832
=
= 182 × 51 − 6889
?2 + 1369
=
2393
2
=
2393 − 1369
?
12
14
27
53
2
? = 32
3. Look at this series: 2, 1, (1/2), (1/4), ... What
number should come next?
(a) 1/3
(b) 1/8
(c) 2/8
(d) 1/16
Department of Extension and Career Guidance
(a)
(b)
(c)
(d)
14
21
15
23
9. Look at this series: 58, 52, 46, 40, 34, ... What
number should come next?
(a)
(b)
(c)
(d)
26
28
30
32
10. Look at this series: 3, 4, 7, 8, 11, 12, ... What
number should come next?
3
Department of Extension and Career Guidance
(a) 7
CHAPTER 1. NUMBER THEORY
17. 9 11 33 13 15 33 17
(b) 10
(a) 19 33
(c) 14
(b) 33 35
(d) 15
(c) 33 19
11. Look at this series: 8, 22, 8, 28, 8, ... What number
should come next?
(a) 9
(b) 29
(c) 32
(d) 34
12. Look at this series: 31, 29, 24, 22, 17, ... What
number should come next?
(a) 15
(d) 15 33
(e) 19 21
18. 2 3 4 5 6 4 8
(a) 9 10
(b) 4 8
(c) 10 4
(d) 9 4
(e) 8 9
19. 17 17 34 20 20 31 23
(b) 14
(c) 13
(d) 12
Directions to Solve: Look carefully for the pattern, and then choose which pair of numbers comes
next.
13. 28 25 5 21 18 5 14
(a) 26 23
(b) 34 20
(c) 23 33
(d) 27 28
(e) 23 28
20. 6 20 8 14 10 8 12
(a) 11 5
(a) 14 10
(b) 10 7
(b) 2 18
(c) 11 8
(c) 4 12
(d) 5 10
(d) 2 14
(e) 10 5
14. 8 11 21 15 18 21 22
(a) 25 18
(b) 25 21
(c) 25 29
(d) 24 21
(e) 22 26
15. 9 16 23 30 37 44 51
(a) 59 66
(b) 56 62
(c) 58 66
(d) 58 65
(e) 54 61
16. 2 8 14 20 26 32 38
(a) 2 46
(e) 14 14
21. 21 25 18 29 33 18
(a) 43 18
(b) 41 44
(c) 37 18
(d) 37 41
(e) 38 41
22. 75 65 85 55 45 85 35
(a) 25 15
(b) 25 85
(c) 35 25
(d) 85 35
(e) 25 75
1. The difference between a number and four-fifth of
the number is 75. What is the number?
(b) 44 50
(a) 375
(c) 42 48
(b) 275
(d) 40 42
(c) 325
(e) 32 26
(d) 525
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4
Department of Extension and Career Guidance
2. The sum of three consecutive odd numbers is 306.
Find out the smallest number?
(a) 201
(b) 301
(d) 19/5
9. Three times the first of three consecutive odd integers is 3 more than twice the third. What is the
value of the third integer?
(c) 101
(a) 25
(d) 401
(b) 35
3. If a number is decreased by 5 and divided by 10,
the result is 15. What could be the result if 5 is
subtracted from the number and then it is divided
by 5?
(a) 10
(c) 45
(d) 15
10. The sum of three consecutive odd numbers is 30
more than the first of these numbers. What is the
last number?
(b) 20
(a) 8
(c) 30
(b) 10
(d) 40
4. If the sum of number and square is 182. Find out
the number?
(a) 11
(c) 16
(d) 14
APTITUDE ANSWERS:
(b) 21
(c) 13
(d) 14
5. What is the unit digit of264102 + 264103 ?
(a) 0
1
A
2
C
(a) 485
(c) 2
(b) 394
(d) 3
(c) 467
(a) 26
(a) 360
(b) 240
(d) 29
(c) 300
(b) 7
(c) 9
(d) 8
8. The product of two numbers is 152 and the sum
of these two numbers is 38. What is the smaller of
these two numbers?
7
D
8
A
9
D
10
C
(d) 700
3. The difference between the squares of two consecutive numbers is 45. The greater number is
(a) 22
(b) 23
(c) 32
(d) 33
4. The difference of two numbers is 13 and 1/7th of
their sum is 9. The numbers are
(a) 25 and 38
(a) 19/8
(b) 27 and 40
(b) 8/19
(c) 41 and 55
(c) 19/10
(d) None of these
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6
C
2. The ration between two numbers is 4:5 and their
sum is 540. The greater of the two numbers is
(c) 28
(a) 6
5
A
(d) 387
(b) 27
7. One-fifth of a number is equal to 3/8 of another
number. If 17 is added to the first number, it becomes four times of the second number. What is
the second number?
4
C
1. What least number must be added to 859622, to
get a number exactly divisible by 456?
(b) 1
6. Twenty six times a positive integer is less than its
square by 56. What is the integer?
3
C
5
Department of Extension and Career Guidance
5. The sum of two numbers is 60 and their difference
is 43. The difference of their squares is
(a) 2580
(b) 2600
(c) 2780
(d) 2860
CHAPTER 1. NUMBER THEORY
12. Of the two numbers, 4 times the first is equal to
6 times the other and the sum of 3 times the first
and 6 times the second is 105. The first number is
(a) 18
(b) 15
(c) 10
(d) 20
6. Three fifth of one fourth of a number is 90. The
number is
(a) 400
(b) 500
(a) 18
(c) 600
(b) 20
(d) 700
7. The sum of two numbers is 17 and sum of their
squares is 145. The numbers are
(a) 9 and 8
8.
(c) 26
(d) 14
14. The sum of three consecutive even numbers is 36.
The middle one is
(b) 8 and 7
(a) 12
(c) 13 and 4
(b) 14
(d) 10 and 7
(c) 10
7
of a certain number is 63. Half of that number
8
is
(a) 36
9.
13. Three numbers are in the ratio 4:5:6 the sum of
the largest and the smallest equals the sum of the
third and 25. The smallest number is
(d) 16
15. If 20 be added to 8 times a certain number, the
result is 10 less than 10 times the number. The
number is
(b) 27
(a) 10
(c) 27.5
(b) 18
(d) 33.5
(c) 12
1
1
of a number subtracted from
of the number
4
3
gives 12. The number is
(a) 144
(b) 169
(c) 196
(d) 225
(d) 15
16. If a and b are positive integers such that ab = 216
then (a − b)a+b−5 is equal to
(a) 47
(b) 81
(c) 27
(d) 216
(c) 18
√
√
√
√
17. By how much 7 3 − 5 7 exceed 5 3 − 9 7 =?
√
√
(a) 2 3 + 4 7
√
√
(b) 2 3 − 4 7
√
√
(c) 4 3 + 4 7
√
√
(d) −4 7 − 2 3
(d) 9
18. The value of (16)0.16 × (16)0.09 is
10. The sum of squares of two numbers is 60 and the
squares of their difference is 44. The product of
the two numbers is
(a) 8
(b) 16
11. A number is as much greater than 31 as is less than
81. The number is
(a) 65
(b) 56
(c) 46
(d) 63
Department of Extension and Career Guidance
(a) 4
(b) 3
(c) 2
(d) 6
√
√
19. If x ÷ 961 = 0.02 then the value of x is
(a) 0.3844
6
Department of Extension and Career Guidance
(b) 3.844
(a) 132
(c) 38.44
(b) 166
(d) 384.4
√
√
√
20. 3 3 48 − 2 3 6 + 3 750 is equal to
√
(a) 6 × 3 4
√
(b) 9 × 3 6
√
(c) 8 × 3 11
√
(d) 7 × 3 5
a
21. If a = 8, b = 2, the find the value of a + b − + ab.
b
(a) 28
(c) 244
(d) None of these
26. If n is odd, n(n2 − 1) is always divisible by
(a) 1
(b) 20
(c) 3
(d) 32
27. If (10n + 2) is divisible by 12 then
(b) 24
(a) n is an odd number
(c) 22
(b) n is an even number
(d) 26
(c) n may be either odd or even number
22. If log10 2 = 0.3010 and log10 7 = 0.8451, then the
value of log10 5.6 is
(a) 0.6342
(d) n may be an irrational number
28. If x is 80% of y, what is the percentage of x in y
is?
(b) 0.7481
(a) 100%
(c) 0.9471
(b) 150%
(d) 0.4471
23. The value of
(c) 1.25%
√
34 +
√
3
125 +
√
4
28 is
(a) 12
(d) 125%
29. The number 0.08 is how many per cent of 40
(b) 18
(a) 0.4
(c) 26
(b) 0.2
(d) None of these
(c) 0.6
24. If the square root of 729 is 27, then the square root
of 0.00000729 is equal to
(d) 0.5
30. If
(a) 0.027
x
3
x + 2y
= , then the value of
equals
2y
2
x − 2y
(b) 0.0027
(a) 3
(c) 0.00027
(b) 7
(d) 0.27
(c) 4
25. If ab = 4 and a + b = 6 then a3 + b3 is
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(d) 5
7
Department of Extension and Career Guidance
CHAPTER 1. NUMBER THEORY
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8
Chapter 2
HCF and LCM
Important Facts and Formulas
• Highest Common Factor (HCF):
The Highest Common Factor (HCF) or Greatest Common Divisor (GCD) of two or more than two numbers
is the greatest number which divides each one of them exactly.
• Least Common Multiple (LCM):
The least number which is exactly divisible by each one of the give numbers is called Least Common Multiple
(LCM).
1. Product of a and b = HCF(a, b) × LCM(a, b).
2. HCF of two or more numbers divides the numbers.
3. The quotients if any must be prime to each other.
4. Sum or difference of two numbers must be divisible by their HCF.
5. HCF(p, q, r) × LCM(p, q, r) 6= p × q × r, where p, q, r are positive integers. However, the following results hold
good for three numbers p, q and r:
LCM(p, q, r) =
p · q · r · HCF(p, q, r)
HCF(p, q) · HCF(q, r) · HCF(p, r)
HCF(p, q, r) =
p · q · r · LCM(p, q, r)
LCM(p, q) · LCM(q, r) · LCM(p, r)
1. Find HCF of 540 and 84.
(a)
(b)
(c)
(d)
(a) 10
(b) 8
(c) 12
25 × 37
27 5 × 35
25 × 38
None of these
4. Find HCF of 2923 and 3239.
(d) 16
(a)
(b)
(c)
(d)
2. Find the HCF of 24,30,36.
(a) 4
(b) 6
(c) 8
39
79
37
47
5. Find the HCF of 5a2 b2 , 20ab3 .
(d) 12
(a) 5ab
(b) 5ab2
3. If x = 25 × 37 × 59 and y = 27 × 38 × 711 , then find
the HCF of and x and y.
9
Department of Extension and Career Guidance
(c) 5a2 b2
CHAPTER 2. HCF AND LCM
(a)
(b)
(c)
(d)
(d) 5a3 b2
6. Find HCF 0f 4x2 y 3 , 6xy 5 .
12abc2
60a2 b2 c2
40a2 b2 c2
15abc
(a) 2xy
1 5 5 10
, , , .
3 6 9 27
(b) 2x2 y 2
14. Find the LCM of
(c) 2xy 3
5
54
5
(b)
27
10
(c)
3
5
(d)
3
15. Two numbers whose sum is 150 have their HCF as
8. The numbers are
(d) 8xy
(a)
3
7. Find the HCF of pm , pm+1 , pm+2 .
(a) pm+1
(b) pm+2
(c) pm
(d) 0
8. Find the HCF of x2 −3x−10, x2 +9x+14, x2 −x−6.
(a) x + 2
(b) x − 2
(c) x − 1
(d) x + 1
2
2
2
9. Find the HCF of p − 4, p + 3p + 2, p + p − 2.
(a) p − 2
(c) (p + 2)(p + 1)
(d) p − 1
1 3 5 7 9
, , , ,
2 4 6 8 10
1
2
1
(b)
10
9
(c)
120
1
(d)
120
73
59
63
53
17. The sum of two numbers is 187 and their HCF is
17. Find how many such pairs can be formed.
(a)
(b)
(c)
(d)
(a)
70, 80
50, 100
120, 30
None of these
16. Find the greatest number which will divide 1050,
1250 and 1650 leaving remainders 43, 31 and 7 respectively
(a)
(b)
(c)
(d)
(b) p + 2
10. Find the HCF of
(a)
(b)
(c)
(d)
2
3
5
None of these.
18. The product of two numbers is 11560 and their
HCF is 34. How many pairs of such numbers can
be formed?
11. Find the LCM of 25, 40.
(a)
(b)
(c)
(d)
(a) 100
(b) 5
(c) 200
(d) 500
2
3
12. Find the LCM of 16x , 24x y
(a) 48xy 2
(b) 48x3 y
(c) 24x3 y
(d) 24xy 2
13. Find the LCM of 10a2 bc, 15abc2 , 20a2 b2 c
Department of Extension and Career Guidance
2
3
4
None of these
19. The product of two numbers is 1875 and their HCF
is 15, their LCM is
(a)
(b)
(c)
(d)
135
1250
125
145
20. The LCM of two numbers is 2420 and their HCF
is 30. If one number is 220, the other number is
10
Department of Extension and Career Guidance
(a) 300
(a) 2
(b) 330
(b) 3
(c) 360
(d) 390
21. The largest number which exactly divides 522,
1276 and 1624 is
(a) 29
(b) 58
(c) 4
(d) 6
22. The largest number which divides 77, 147 and 252
to leave the same remainder in each case is
(a) 9
(b) 15
(c) 25
(d) 35
23. By which smallest number 1323 must be multiplied
so that it becomes a perfect cube
Department of Extension and Career Guidance
(c) 5
(d) 7
24. Which is the greatest?
(a)
(b)
(c)
(d)
√
3
√
4
√
√
4
5
2
3
25. The least number when divided by 4, 6, 8, 12 and
16 leaves a remainder 2 in each case is
(a) 46
(b) 50
(c) 48
(d) 56
11
Department of Extension and Career Guidance
CHAPTER 2. HCF AND LCM
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12
Chapter 3
Ages
Important Facts and Formulae
Problems based on Ages is an very important topic which is given most of the competative exams. You can
easily solve all kind of aptitude questions based on Problems on ages by practicing regularly. Before going to slove
the problem on ages you need to know the linear equation which help in math but first you are do traditional
process than you learn shortcut tricks.
Anything we learn in our school days was basics and that is well enough for passing our school exams. For this
we need our basics but also we have to learn something new. That’s where shortcut tricks are comes into action.
This type of problem are given in Quantitative Aptitude which is a very essential paper in banking exam. Under
below given some more example for your better practice. In competative examination there are three situation
based questions are given which are given below:
1. Present Age
2. Years ago Age
3. Hence years age
examples
1. The ratio of present ages of A and B is 2:3. The present age of A is 30 years. Find the age of B after 5 years.
Answer:
Step-1: A:B present age ratio = 2:3 and A=30 years.
A
2
30 × 3
Step-2:
= ⇒B=
= 45.
B
3
2
Step-3: B age after 5 years = 45+5 = 50.
2. Niloy is as younger to Ganesh as he is older to Dev. If the sum of the ages of Ganesh and Dev is 58 years.
What is Niloy age?
Answer:
Step-1: G - N = N - D.
Step-2: G + D = 2N = 58 years.
Step-3: N = 29 years.
3. Ratio of ages of M and N 4 years ago was 3:5. If the sum of present ages of M and N is 64 years, then find
the present ages of M and N.
Answer: M=25 & N=39.
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Department of Extension and Career Guidance
CHAPTER 3. AGES
4. At present, the ratio between the ages of Anil and Anu is 4:3. After 4 years, Anil’s age will be 24 years.
What is the age of Anu at present?
Answer: 15.
5. The total age of Gangotri, Sabir and Bibhas is 96 years. 10 years ago, the ratio of their ages was 2:4:5. What
is the present age of Bibhas?
Answer: 40
6. Present age of Ramesh and Suresh are in the ratio 5:6. Six years hence, the ratio of their ages will becone
6:7. What is Ramesh present age? Answer: 30
7. Seven years ago, the age ratio of Sonu and Monu was 6:5. Three years hence, the ratio of their ages will be
11:10. What is Monu’s age at present?
Answer: 17
8. 12 years hence, Rahul will be just five times as old as he was 12 years ago. His present age is?
Answer: 8.
EXERCISES
1. The age of mother 10 years ago was thrice as the
age of his daughter. 10 years hence mothers age
will be twice that of his daughter. What is the
ratio of their present ages?
(a) 7:3
(b) 3:7
(c) 6:7
(d) 7:6
2. The total age of P and Q is 15 years more than the
total age of Q and B. B is how many years younger
than P?
(a) 10
(b) 12
(c) 13
(d) 15
3. Raju is as much younger than Sonu as he is older
than Tanu. If the sum of the ages of Sonu and
Tanu is 45 years, what is the difference between
the ages of Sonu and Raju?
(a) 45
(b) 50
(c) Can’t be determined
(d) 55
4. Soniya got married 7 years ago. Her present age
is 6/5 times her age at the time of marriage. Her
brother was 5 years younger to her at the time
of marriage. What is the age of her brother at
present?
(a) 35
(b) 36
(c) 37
Department of Extension and Career Guidance
(d) 38
5. Mother is aged 3 times more than her son Sanjay.
After 12 years she would be 2 and a half times
of Sanjays age. After further 12 years how many
times would she be Sanjays age?
(a)
(b)
(c)
(d)
1
2
3
4
6. A mother said to her son, I was as old as you are
at present at the time of your birth. If the mothers
age is 35 years now the sons age 6 years back will
be how many years?
(a)
(b)
(c)
(d)
11.5
12.5
13.5
14.5
7. The age of Rajeev is 1/6th of his mothers present
age. Rajeevs mother age will be twice of his sister
Kamalas age after 10 years. If Kamalas 7th birthday was celebrated three years before, then what
is Rajeevs present age?
(a)
(b)
(c)
(d)
5
4
12
9
8. Sindus was asked about her age in years. Her reply was, Take my age 3 years hence, multiply it
by 3 and then minus 3 times. Here age of mine 3
years ago and you will come to know how old I am.
What was the age of Sindhu?
(a) 12
(b) 18
(c) 19
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Department of Extension and Career Guidance
(d) 20
9. If Priya was 1/3rd as old as Peter 5 years back and
Priya is 17 years old now, How old is Priya now?
(a) 41
(b) 51
(c) 42
Manu. The current sum of the ages of Tanu and
Manu is 57. How old is Manu right now?
(a) 15
(b) 18
(c) 20
(d) 25
(d) 43
APTITUDE ANSWERS:
10. 12 years from now Tanu will be twice as old as 1. A 2. D 3. C 4. C 5. B 6. A 7. A 8. B 9. A 10. A
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15
Department of Extension and Career Guidance
CHAPTER 3. AGES
Department of Extension and Career Guidance
16
Chapter 4
Average
Important Facts and Formulae
1. Average =
Sum of observations
.
Number of observations
2. Suppose a man covers a certain distance at x kmph and an equal distance at y kmph. Then, the average
2xy
speed during the whole journey is
kmph.
x+y
3. When a person leaves a group and another person joins the group in the place of person left then,
(a) In the case of increase in average age Age of new comer = Age of the person left + number of
persons in the group × increase in average age.
(b) In the case of decrease in average age Age of new comer = Age of the person left - number of
persons in the group × decrease in average age.
4. When a person joins a group without replacing any person from that group, then
(a) In the case of increase in average age Age of new comer = Previous average age + number of
persons in the group × increase in average age.
(b) In the case of decrease in average age Age of new comer = Previous average age - number of
persons in the group × decrease in average age.
5. When a person leaves the group but nobody joins the group, then
(a) In the case of decrease in average age Age of person left = Previous average age - number of
present persons in the group × decrease in average age.
(b) In the case of increase in average age Age of person left = Previous average age + number of
present persons in the group × increase in average age.
6. Geometric Mean (GM) of x1 , x2 , . . . , xn is given by
√
GM = n x1 × x2 × · · · × xn .
1. The average of first five multiples of 5 is
(a) 21
(a) 10
(b) 20
(b) 15
(c) 19
(c) 20
(d) 22
(d) 25
3. If x, y, x are three consecutive even numbers, then
their average is
2. The average of 3 numbers is 15 and that of the first
two is 12. The third number is
17
(a) x + 2
Department of Extension and Career Guidance
xy + yz
3
2x + 3
(c)
3
(d) None of these.
(b)
4. If a, b, c, d, e are five consecutive odd numbers,
what will be their average?
CHAPTER 4. AVERAGE
(d) 24
8. The average score of a cricker for 10 matches is 49.7
runs. If the average for the first seven matches is
45. What is the average for last 3 matches?
(a) 40.5
(b) 30.66
(a) 5(a + 4)
(c) 65.65
(b) (a + 4)
abcde
(c)
5
(d) Data inadequate
(d) 60.66
5. What fraction shold be subtracted from the sum
1
2
of
and
to that the average of these numbers
8
3
1
comes to ?
6
(a)
(b)
(c)
(d)
17
24
7
24
11
16
None of these
6. The average of 8 members is 9. What is the 9th
member so that average becomes 10?
(a) 17
(b) 20
9. Number B is 70 more than twice the number A.
Number C is 10 more than twice the number B. If
the average of A, B, C is 120, what is the value of
C?
(a) 130
(b) 230
(c) 250
(d) 175
10. The average age of 12 girls and their teacher is 14
years. If the teacher’s age is excluded the average
reduces by one. What is the teacher’s age?
(a) 20
(b) 36
(c) 26
(d) 38
11. The average of first five multiples of 9 is
(c) 18
(a) 25
(d) 21
(b) 27
7. The average of 13 results is 60. If the average of
seven results is 57 and that of last seven is 58, find
the 7th result.
(c) 31
(d) 22
12. (a)
(a) 31
(b)
(b) 25
(c)
(c) 20
(d)
Department of Extension and Career Guidance
18
Chapter 5
Alligation and Mixture
Important Formulas
1. Alligation: It is the rule that enables us to find the ratio in which two or more ingredients at the given price
must be mixed to produce a mixture of desired price.
2. Mean Price: The cost of a quantity of the mixture is called the mean price.
3. Rule of Allegation: If two ingredients are mixed, then
(C.P. of dearer) - (Mean price)
Quantity of cheaper
=
Quantity of dearer
(Mean price) - (C.P. of cheaper)
Quantity of cheaper(c)
Quantity of dearer(d)
Mean price (m)
(d-m)
Therefore,
(m-c)
(Cheaper Quantity):(Dearer quantity)= (d-m):(m-c).
4. Suppose a container contains x units of liquids from which
y units are taken out and replaced by water. After
n
n operations, the quantity of pure liquid = x 1 − xy units.
Examples:
1. In what ratio must a grocer mix two varieties of pulses costing Rs. 15 and Rs. 20 per kg respectively so as
to get a mixture worth Rs. 16.50 kg?
2. Wheat worth Rs. 126 per kg and Rs. 135 per kg are mixed with a third variety in the ratio 1:1:2. If the
mixture is worth Rs. 153 per kg, what is the price of the third variety per kg?
3. In what ratio must rice at Rs. 9.30 per kg be mixed with rice at Rs. 10.80 per kg so that the mixture be
worth Rs. 10 per kg?
4. A milk vendor has 2 cans of milk. The first contains 25% of water and the rest milk. The second contains
50% water. How much milk should he mix from each of the containers so as to get 12 litres of milk such that
the ratio of water to milk is 3:5?
19
Department of Extension and Career Guidance
CHAPTER 5. ALLIGATION AND MIXTURE
5. 4 kg of rice at Rs. 5 per kg is mixed with 8 kg of rice at Rs. 6 per kg. Find the average price of the mixture?
6. 5 kg of rice at Rs. 6 per kg is mixed with 4 kg of rice to get a mixture of costing Rs. 7 per kg. Find the price
of the costlier rice?
7. A butler stole wine from a wine shop which contained 40% of spirit and he replaced, what he had stolen by
wine containing only 16% spirit. The shop has then the wine having strength of 24% only. How much did
the butler steal?
8. The average weekly salary per head of the entire staff of a factory consisting of supervisors and laborers is Rs.
60. The avarage salary of the supervisor is Rs. 400 and that of laborers is Rs. 56. Giveb that the number of
supervisors is 12. Find the number of laborers in the factory.
9. The cost of type 1 onions is Rs. 15 per kg and type 2 onions is Rs. 20 per kg. If both type 1 and type 2 are
mixed in the ratio of 2:3, then the price per kg of the mixed variety of onion is?
10. A jar full of whisky contains 40% alcohol. A part of thus whisky is replaced by another containing 19%
alcohol and now the percentage of alcohol was found to be 26%. The quantity of whisky replaced is?
Answers
1.
2.
3.
4.
5.
3.5 : 1.5
Rs. 175.50
8: 7
6 litres
Rs. 5.66
Department of Extension and Career Guidance
6. Rs. 8.25 per kg
7. 2/3
8. 1020
9. Rs. 18 per
10. 2/3
20
Chapter 6
Boats and Streams
Important Facts and Formulae
• First thing: The speed of water or stream that denoted by v kmph.
• Second thing: Speed of boat or boatman in calm water which we denoted by u kmph.
• Third thing: In water, the direction along the stream is called downstream.
Speed downstream = (u + v) kmph.
• Fourth thing: In water, the direction of boat against the stream is called upstream.
Speed upstream = (u − v) kmph.
• If the speed downstream is x kmph and the speed upstream is y kmph, then:
1. Speed in still water = 21 (x + y) kmph.
2. Rate of stream = 12 (x − y) kmph.
21
Department of Extension and Career Guidance
CHAPTER 6. BOATS AND STREAMS
Department of Extension and Career Guidance
22
Chapter 7
Calender
Important Facts and Formulas
We are supposed to find the day of the week on a given date. For this, we use the concept of odd days.
1. Odd days: In a given period, the number of days more than the complete weeks are called odd days.
2. Leap year:
(a) Every year divisible by 4 is a leap year, if it is not a century.
(b) Every 4th century is a leap year and no other century is a leap year.
(c) A leap year has 366 days = 52 weeks + 2 odd days.
Examples:
i. Each of the years 1948, 2004, 1676 etc. is a leap year.
ii. Each of the years 400, 800, 1200, 1600, 2000 etc. is a leap year.
iii. None of the years 2001, 2002, 2003, 2005, 1800, 2100 is a leap year.
(d) Ordinary year:
i. The year which is not a leap year is called an ordinary year.
ii. An ordinary year has 365 days.
(e) Counting of odd days:
i. 1 ordinary year = 365 days = 52 weeks + 1 days.
∴ 1 ordinary year has 1 odd day.
ii. 1 leap year = 366 days = 52 weeks + 2 days.
∴ 1 leap year has 2 odd days.
iii. First 100 years (From 0001 to 0100) = 76 ordinary years + 24 leap years
.
= (76 × 1 + 24 × 2) odd days
.
= 124 odd days
.
= 17 weeks + 5 odd days
.
= 5 odd days.
iv. First 200 years (From 0001 to 0200) = (5 × 2)= 10 odd days = 3 odd days.
v. First 300 years (From 0001 to 0300) = (5 × 3)= 15 odd days = 1 odd day.
vi. First 400 years (From 0001 to 0400) = (5 × 4 + 1)= 21 odd days = 0 odd day.
(f) Day of the week related to odd days:
No. of day
Day
0
Sun
1
Mon
2
Tues
3
Wed
4
Thurs
5
Fri
Concept: How to find the day of the any year between 1900 - 2000:
(a) Write the last 2 digits of the year. Let it be A.
23
6
Sat
Department of Extension and Career Guidance
CHAPTER 7. CALENDER
(b) Write the number of leap years from 1900 to given year. Let it be B.
(c) Let month key value be C.
Month
January
February
March
April
May
June
July
August
September
October
November
December
Key value
1
4
4
0
2
5
0
3
6
1
4
6
(d) Let Date be D.
(e) Find Remainder
A+B+C +D
=R.
7
R-value
1
2
3
4
5
6
0
Day
(Ordinary year)
Sunday
Monday
Tuesday
Wednesday
Thursday
Friday
Saturday
Department of Extension and Career Guidance
Day
(Leap year)
Saturday
Sunday
Monday
Tuesday
Wednesday
Thursday
Friday
24
Chapter 8
Clock
Important Facts and Formulas
1. In every hour
(a) Both the hands coincide once.
(b) The hands are straight (points in opposite direction) once. In this position, the hands are
30 minute spaces apart.
4. The minute hand of a clock overtake the hour hand
at interval of M minutes of correct time. The clock
gains or losses in a day by
60 × 24
720
−M
=
minutes.
11
M
(c) The hands are twice at right angles.
Using Common sense:
2. The minute hand moves through 6◦ in each minute
Concept 1:
◦
where as the hour hand moves through 21 in each
minute. Thus, in one minute, the minute hand
◦
gains 5 12 than the other hand.
• 12 hours = 360◦
• 1 hour = 30◦
3. Minute hand moves 12 times as fast as the hour
hand.
4. If a clock indicates 6.10 when the correct time is
6, it is said to be 10 minutes too late.
5. If a clock indicates 5.50 when the correct time is
6, it is said to be 10 minutes too slow.
Short cut methods:
• 60 minutes = 30◦
◦
1
• 1 minute =
2
1. Type-I: From Time period to Angle:
Steps:
(a) Find the number of hours n between hour
hand and minute hand.
1. Between H and H + 1 O’ clock, the two hands of a
clock are M minutes apart at (5H ∓ M ) 12
11 minutes
past H O’clock.
(b) For 1 hour, angle is 30◦ , find the angle for n
hours. Let it be Θ1 .
(c) Find the angle of hour hand for given minutes.
Let it be Θ2 .
2. When the minute hand is behind the hour hand,
the angle between the two hands at M minutes
past H O’clock
M
M
= 30 H −
+
degree.
5
2
(d) Then the required angle is Θ1 − Θ2 .
Example 1: Find the angle between the two
hands of the clock for the time 3.40 pm.
Solution:
3. When the minute hand is ahead the hour hand, the
angle between the two hands at M minutes past H
O’clock
M
M
= 30 H −
−
degree.
5
2
(a) The number of hours between the two hands
= 5 hours
(b) ∴ Θ1 = 5 × 30◦ = 150◦ .
◦
1
= 20◦ .
(c) Θ2 = 40 ×
2
25
Department of Extension and Career Guidance
(d) Then the required angle is
Θ1 − Θ2 = 150◦ − 20◦ = 130◦ .
2. Type-II: Coincidence:
Concept 2:
• 1 hour = 5 divisions
D
5
1
• Speed of hour hand =
=
=
division
T
60
12
per minute.
60
D
=
= 1division
• Speed of minute hand =
T
60
per minute.
• Both the hands are travelling in same direction.
∴ Relative speed is
60
1−
1
12
6. The minute hand of a clock overtakes the
hour hand at intervals 65 minutes of the correct time. How much a day does the clock
gain or loss?
7. A watch which gains uniformly, is 5 minute.
slow at 8 o’clock in the morning on sunday
and it is 5 min. 48 sec. fast at 8 p.m. on
following Sunday. When was correct?
• 12 hours = 60 divisions
Sm − Sh =
CHAPTER 8. CLOCK
= 60 ×
12
.
11
• Both hands will coincide after every 1.05.5/11
hours.
Example 2: At what time, after 3 o’clock both
hands will coincide?
Solution:
4
3 × (1.05.5/11) = 3.15.15/11 = 3 hours 16
min11
utes.
8. A clock is set right at 5 a.m. The clock loses
16 minutes in 24 hours. What will be the
true time when the clock indicates 10 p.m.
on 4th day?
9. A clock is set right at 8 a.m. The clock gains
10 minutes in 24 hours. What will be the
true time when then clock indicates 1 p.m.
on the following day?
10. What is the angle between the minute and
hour hands of a clock at 7:35?
Answers:
◦
5
2
47 21 , 10 10
11 min past 2, 5 11 min past 4 and 38 11
10
min past 4, 10 11 min past 8, 24 min past 5 and
5
10
31 11
min past 5, 10 43
minutes gains in 24 hours,
20 min. past 7 p.m. on Wednesday, 11 p.m., 48
min. past 12, 17.5◦
3. Type-III: From angle to Time period:
Concept 3:
• 60 divisions = 360◦
• 1 division = 6◦
Example 3: At what time, between 5-6 pm will
both hands makes the following angles 60◦
? Solution:
Questions:
1. Find the angle between the hour hand and
the minute hand of a clock when the time is
3.25?
2. At what time between 2 and 3 o’clock will
the hands of a clock be together?
3. At what time between 4 and 5 o’clock will
the hands of a clock be at rightangle?
4. At what time between 8 and 9 o’clock will
the hands of a clock be in the same straight
line but not together?
5. At what time between 5 and 6 o’clock are
hands of a clock 3 minutes apart?
Department of Extension and Career Guidance
26
Department of Extension and Career Guidance
Exercise:
1. A clock is started at noon. By 10 minutes
past 5, the hour hand has turned through
(A) 145◦
(B) 150◦
◦
(C) 155
(D) 160◦
2. An accurate clock shows 8 o’clock in the
morning. Through how many degrees will
the hour hand rotate when the clock shows
2 o’clock in the afternoon?
(A) 144◦
(B) 150◦
◦
(C) 168
(D) 180◦
3. At 3.40, the hour hand and the minute hand
of a clock form an angle of
(A) 120◦
(B) 125◦
(C) 130◦
(D) 135◦
4. The angle between the minute hand and the
hour hand of a clock when the time is 8.30,
is
(A) 80◦
(B) 75◦
(C) 60◦
(D) 105◦
5. The angle between the minute hand and the
hour hand of a clock when the time is 4.20,
is
(A) 0◦
(B) 10◦
◦
(C) 5
(D) 20◦
6. At what angle the hands of a clock are inclined at 15 min. past 5?
◦
(B) 64◦
(A) 58 21
◦
1◦
(C) 67 2
(D) 72 12
7. The reflex angle between the hands of a
clock at 10.25 is
◦
(A) 180◦
(B) 192 12
◦
(C) 195◦
(D) 197 12
8. How many times do the hands of a clock coincide in a day?
(A) 20
(B) 21
(C) 22
(D) 24
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9. How many times do the hands of a clock are
straight in a day?
(A) 22
(B) 24
(C) 44
(D) 48
10. How many times do the hands of a clock are
at rightangle in a day?
(A) 22
(B) 24
(C) 24
(D) 48
11. How many times do the hands of a clock are
straight line but opposite in direction in a
day?
(A) 20
(B) 22
(C) 24
(D) 48
12. How much does a watch lose per day, if its
hands coincide every 64 minutes?
5
8
min
(B) 36 11
min
(A) 32 11
(C) 90 min.
(D) 96 min.
13. At what time, in minutes, between 3 and 4
o’clock, both the needles will coincide each
other?
4
1
min
(B) 12 11
min
(A) 5 11
4
4
min.
(C) 13 11 min. (D) 16 11
14. At what time between 7 and 8 o’clock, both
the needles will in straight but not together?
. . . . . . min. past 7
2
(A) 5
(B) 5 11
3
5
(C) 5 11
(D) 5 11
15. A watch which gains uniformly 2 minutes
low at noon on Monday and 4 min. 48 sec.
fast at 2 p.m. on the following Monday.
When was it correct?
(A) 2p.m. on Tuesday
(B) 2p.m. on Wednesday
(C) 3p.m. on Thursday
(D) 1p.m. on Friday.
27
Department of Extension and Career Guidance
CHAPTER 8. CLOCK
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28
Chapter 9
Mensuration
Important Facts and Formulas
1. Perimeter: Perimeter is the distance covered along the boundary forming a closed figure when you go round
the figure once.
a rectangle = 2 × (length + breadth).
a square = 4 × length of a side.
an equilateral triangle = 3× length of a side.
a circle = 2 × π × radius = π × diameter
perimeter of a circle
.
Where π = 3.14 ≈ 22
7 =
diameter
2. Area: The amount of surface enclosed by a closed figure is called its area.
(a)
(b)
(c)
(d)
Perimeter
Perimeter
Perimeter
Perimeter
(a)
(b)
(c)
(d)
(e)
(f)
Area
Area
Area
Area
Area
Area
of
of
of
of
of
of
of
of
of
of
a rectangle = length × breadth.
a square = side × side.
triangle = 12 × base × height.
parallelogram = base × height.
a circle = π × radius2 .
a trapezium = 12 × h × (a + b).
3. Surface Area:
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
(i)
Surface Area of a Cuboid = 2(lb + bh + hl)
Surface Area of a Cube = 6a2
Curved Surface Area of a Cylinder = 2πrh
Total Surface Area of a Cylinder = 2πrh + 2πr2 = 2πr(h + r)
Curved Surface Area of a Cone = πrl
Total Surface Area of a Cone = πrl + πr2 = πr(l + r).
Surface Area of a sphere = 4πr2
Curved Surface Area of a Hemisphere = 2πr2 .
Total Surface Area of a Hemisphere = 3πr2 .
4. Volume:
(a)
(b)
(c)
(d)
(e)
Volume
Volume
Volume
Volume
Volume
of
of
of
of
of
a
a
a
a
a
Cuboid = lbh
Cube = a3
Cylinder = πr2 h
Cone = 13 πr2 h
Sphere = 43 πr3
29
Department of Extension and Career Guidance
(a) The area of the room is 2970 sq. m. If its length
is 66 m, find its breadth.
(a)
(b)
(c)
(d)
35
45
55
58
m
m
m
m
(b) Area of the square is 841 sq. m. Find its perimeter.
(a)
(b)
(c)
(d)
112
116
118
120
m
m
m
m
(c) A rectangular field is 12 m long and 5 m broad.
Find the length of its diagonal.
(a)
(b)
(c)
(d)
13
18
19
22
m
m
m
m
(d) The area of the square field is 7200 sq. m. Find
the length of its diagonal.
(a)
(b)
(c)
(d)
110
120
130
140
8.74
8.47
6.74
5.64
sq.
sq.
sq.
sq.
(a)
(b)
(c)
(d)
28
30
31
25
cm
cm
cm
cm
(g) Find the area of a parallelogram whose base is
6.2 cm and the perpendicular distance from the
other side on the base is 3.6 cm
(a)
(b)
(c)
(d)
(h) (a)
(b)
(c)
(d)
(i) (a)
(b)
(c)
(d)
(j) (a)
(b)
(c)
(d)
m
m
m
m
(e) Find the area of a triangle whose base is 4.6 m
and height is equal to 3.8 cm.
(a)
(b)
(c)
(d)
CHAPTER 9. MENSURATION
cm.
cm.
cm.
cm.
(f) The hypotenuse of a right-angled triangle is 13
cm and the base is 5 cm. Find its perimeter
Department of Extension and Career Guidance
(k) (a)
(b)
(c)
(d)
(l) (a)
(b)
(c)
(d)
30
Chapter 10
Permutation
Important Facts and Formulae
1. When two tasks are performed in succession, i.e.,
they are connected by an AND, to find the the
total number of ways of performing the two tasks,
you have to MULTIPLY the individual number
of ways.
2. When only one of the two tasks is performed, i.e.,
the tasks are connected by an OR, to find the total number of ways of performing the two tasks you
have to ADD the individual number of ways.
5. In how many ways can you send 5 children to 7
classrooms?
6. Such that no two children are in the same class?
7. Such that at least two children are in the same
class?
8. How many three digit numbers are there?
9. Such that the digit 6 does not appear?
10. Such that the digit 0 does not appear?
3. Examples:
11. How many 3 digit even numbers can be formed
from 0, 1, 2, 3, 4, 5?
(a) If a thief wants to enter via a door or window,
he can do it in (d + w) ways.
12. In how many ways can 8 children sit on 8 seats
numbered A,B,C,D,E,F,G,H?
(b) If a thief wants to enter via a door and leaves
via a window, he can do it in (d × w) ways.
13. Such that Ramesh is on seat C?
Questions
14. Such that Ramesh is on seat B and Suresh is on
seat C?
1. You have 20 shirts and 10 pants. In how many
ways can you decide what to wear?
15. Such that Ramesh is just to the left of Suresh?
16. Such that Ramesh and Suresh are together?
2. You have 20 shoes and 10 slippers. In how many
ways can you decide what to wear?
17. Such that Ramesh is to the left of Suresh?
3. You have 20 shirts, 10 pants, 20 shoes & 10 slippers. In how many ways can you decide what to
wear?
4. In how many ways can you invite 5 friends a party?
31
18. Such that Ramesh and Suresh are at the corners?
19. Such that Ramesh, Suresh & Dinesh are together?
20. Such that Ramesh is to the left of Suresh & Suresh
is to the left of Dinesh?
Department of Extension and Career Guidance
CHAPTER 10. PERMUTATION
Department of Extension and Career Guidance
32
Chapter 11
Percentage
Important Facts and Formulae
1. Concept of Percentage: By a certain percent, we mean that many hundredths. Thus, x percent means
x hundredths, written as x%.
2. To express x% as a fraction: We have, x% =
x
.
100
20
1
= .
100
5
a
a a
3. To express
as percent: We have, =
× 100 %.
b
b
b
1
1
Thus, =
× 100 % = 25%.
4
4
Thus, 20% =
4. If the price of a commodity increases by R%, then the reduction in consumption so as not to increase the
expenditure is
R
× 100 %.
100 + R
5. If the price of a commodity deccreases by R%, then the increase in consumption so as not to increase the
expenditure is
R
× 100 %.
100 − R
6. Results on Population: Let the population of a town be P now and suppose it increase at the rate of R%
per annum, then
n
R
(a) Population after n years = P 1 +
100
P
n
(b) Population n years ago = R
1+
100
7. Results on Depreciation: Let the present value of a machine be P . Suppose it depreciates at the rate of
R% per annum. Then:
n
R
(a) Value of the machine after n years = P 1 −
100
P
n
(b) Value of the machine n years ago = R
1−
100
33
Department of Extension and Career Guidance
CHAPTER 11. PERCENTAGE
R
× 100 %.
8. (a) If A is R% more than B, then B is less than A by
100 + R
R
(b) If A is R% less than B, then B is more than A by
× 100 %.
100 − R
Successive Percentage:
(a) Concept:
• Initial value = 100.
• After 10% = 100 + 10 = 110.
• After again 10% = 110 + 11 = 121.
10 × 10
• 21 = 10 + 10 +
%.
100
• Formula:
ab
%
a+b+
100
Example 1: In a rectangle
•
•
•
•
Length increase = 10%
Breadth increase = 20%
Overall % change in area = ?
Area = Length × Breadth
10 × 20
% = 32%
10 + 20 +
100
Example 2: In a square
• side increase = 30%
• Overall % change in area = ?
• Area = side × side
30 × 30
30 + 30 +
% = 69%
100
Example 3:
• Price increase = 40%
• Consumption deccrease = 20%
• Overall % change in expenditure = ?
•
40 × (−20)
40 − 20 +
% = 12%
100
Example 4: In a cylinder
•
•
•
•
Radius increase = 10%
Height increase = 00%
Overall % change in Volume = ?
V =π×r×r×h
10 × 10
10 + 10 +
% = 21%
100
21 × 30
21 + 30 +
% = 57.3%
100
Example 5: 3 successive discounts
• 10%, 20% and 30%
Department of Extension and Career Guidance
34
Department of Extension and Career Guidance
• Single discount % = ?
−10 × −20
−10 − 20 +
% = −28%
100
−28 × −30
% = −49.6%
−28 − 30 +
100
Note:
(a) In case of SI, Rate of interest → Constant every year.
(b) In case of CI, Rate of interest → Successive every year.
Example 6: About SI and CI
• In two years, CI - SI = 12.
• R%=20%
• P=?
20 × 20
% = 44%
• CI= 20 + 20 +
100
• SI= (20+20)%=40%.
• CI - SI = 4.
100
× 12 = 300.
• P =
4
Concept:
Example 1:
• 122 = 12 × 12 = 144.
2
•
= 20%.
10
20 × 20
• 20 + 20 +
% = 44%
100
Example 2:
• (1.02)4 = 1.02 × 1.02 × 1.02 × 1.02 =?.
0.02
•
= 2%.
1
2×2
• 2+2+
% = 4.04%
100
4×4
• 4+4+
% = 8.16% = 0.0816
100
• (1.02)4 = 1.02 × 1.02 × 1.02 × 1.02 = 1.0816.
exercises
1. An HR company employs 4800 persons, out of
which 45% are males and 60% of the males are
25 years and older. How many males are younger
than 25 years?
(a) 2649
(b) 2160
(c) 864
(d) 1296
(e) None of these
exercises
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35
Department of Extension and Career Guidance
1. In a company of 2000 employees 60% are males of
whom 20% are programmers. If of all the employees, 25% are programmers then what percent of
the females of the town are male?
CHAPTER 11. PERCENTAGE
(b) 54.1
(c) 50.1
(d) 56.1
7. The population of a town 2 years ago was 65,000.
Due to migration the population decreases at the
rate of 5% per annum. What is the present population of the town?
(a) 21.5
(b) 32.5
(c) 31.5
(d) 41.5
(a) 58662
2. The price of the book is increased by 25% and then
reduced by 25%. What is the final price of the
book?
(b) 57772
(c) 56009
(d) 57000
(a) 91.75
8. The value of machine depreciates at the rate of 25%
every year. It was purchased three years ago. If
its present value is Rs. 8500 what was its purchase
price?
(b) 92.75
(c) 95.75
(d) 93.75
3. The price of an shirt was increased by r%. Later
the new price was decreased by r%. If the latest
price was Rs. 1 then what is the original price?
(a) 20148.14
(b) 25000.14
(c) 23123.50
(a) r
(d) 25250.15
(b) 2r
(c) 100/(100 − r2 )
2
(d) 10000/(10000 − r )
4. Raju has made an investment in the share market.
He had the income in the year 2009 such that he
had earned a profit of 20% on his investment in
the business. In the year 2010 his investment was
less by Rs. 5000 but still he had the same income
as that in 2009. Thus the profit % earned in 2009
increased by 5%. What was Raju’s investment?
(a) 105,000
(b) 125,000
(c) 135,000
(d) 102,500
5. In a fraction if the numerator is increased by 60%
and the denominator is increased by 40% then
what fraction of the original is the new fraction?
9. Arjuns cricket score has ups and downs in each
year. His score increased two consecutive years
consistently by 25% and in the third year it decreases by 20%. Again in the next two years it
increases by 15% each year and decreases by 10%
in the third year. If we start counting from the
year 1998 approximately what will be effect of his
score in 2002?
(a) 55.25
(b) 56.25
(c) 57.25
(d) 58.25
10. The total population of a school is 4000 in 2010.
In 2011 the number of boys increased by 10% and
the number of girls increased by 15% and consequently the total population of the school becomes
5000. Find out the number of boys?
(a) 7/8
(a) 5000
(b) 8/7
(b) 8000
(c) 9/7
(d) 9/8
6. If price rises at the rate of 7% per annum what will
be Rs. 49 cost at the end of two years?
(a) 55.1
Department of Extension and Career Guidance
(c) 7000
(d) 6000
APTITUDE ANSWERS:
1) B 2) D 3) D 4) A 5) B 6) D 7) A 8) A 9) B 0) B
36
Chapter 12
Partnership
Important Facts and Formulae
1. Partnership: when two or more than two persons run a business jointly, they are called partners and the
deal is known as partnership.
2. Ratio of Division of Gains:
(a) When investments of all the partners are for same time, the gain or loss is distributed among the partners
in the ratio of their investments.
Suppose A and B invest Rs. x and Rs. y respectively for a year in a business, then at the end of the
year:
( A’s share of profit) : (B’s share of profit) = x : y.
(b) When investments are for different time periods, then equivalent capitals are calculated for a unit of
time by taking (capital × number of units of time). Now, gain or loss is divided in the ratio of these
capitals.
Suppose A invests Rs. x for p months and B invests Rs. y for q months, then
( A’s share of profit) : (B’s share of profit) = xp : yq.
3. Working and Sleeping Partners: A partner who manages the business is known as a working partner
and the one who simply invests the money is a sleeping partner.
37
Department of Extension and Career Guidance
CHAPTER 12. PARTNERSHIP
Department of Extension and Career Guidance
38
Chapter 13
Probability
Important Facts and Formulas
Definitions:
1. An Experiment E is called a random experiment (or trail) if
(a) all possible outcomes of E are known in advance
(b) it is not possible to predict which of the outcomes will occur on a particular trail
(c) the experiment can be repeated infinite number of times under identical condition
Examples:
(a) Rolling an unbiased dice.
(b) Tossing a fair coin.
(c) Drawing a card from a pack of well-shuffled cards.
(d) Picking up a ball of certain colour from a bag containing balls of different colours.
Details:
(a) When we throw a coin, either a Head (H) or a Tail (T) appears.
(b) A dice is a solid cube, having 6 faces, marked 1, 2, 3, 4, 5, 6 respectively. When we throw a die, the
outcome is the number that appears on its upper space.
(c)
• A pack of cards has 52 cards.
• It has 13 cards (A, 2, 3, 4, 5, 6, 7, 8, 9, 10, J, Q and K) of each suit, namely Spades (♠),
Clubs (♣), Hearts (♥) and Diamonds (♦).
• Cards of spades and clubs are Black cards.
• Cards of hearts and diamonds are red cards.
• There are 4 honours of each suit. These are Aces (A), Kings (K), Queens (Q) and Jacks (J).
These are called face cards.
2. The set of all possible outcomes of a random experiment E is called the sample space of the experiment
and it is denoted by S.
3. The outcomes or results of a random experiment is called events connected with the experiment. In other
words, the subsets of sample space is called event.
4. An event of a given experiment is called impossible event if it can never happen in any trail of the random
experiment. The null set in S is called Impossible event.
5. An event of a random experiment is called sure event or certain event, if it happens in every trail of the
random experiment. The sample space S is called Sure event or Certain event.
39
Department of Extension and Career Guidance
CHAPTER 13. PROBABILITY
6. Two events are said to be mutually exclusive if they can not happen simultaneously at any trail of the
experiment.
Example: When we roll a die the events 1, 2, 3 and 4, 5, 6 are mutually exclusive event
7. A collection of events is said to be exhaustive if in every trail of the given random experiment E atleast one
of them must occur (not neccssarily the same in each trail).
Example: When a die is rolled, the set of events 1, 2, 3, 2, 3, 5, 5, 6 and 4, 5 are exhaustive events.
8. Two events we said to be equally likely if none of them can be expected in preference to the other.
Example: When a coin is tossed, the events head and tail are equally likely.
9. If the same space S of a random experiment E contains n mutually exclusive, exhaustive and equally likely
outcomes of an experiment of which m of them are favourable to an event A, then the probability of A is
defined as
m
P (A) = .
n
In other words,
let S be the sample space and A be an event associated with a random experiment. Let n(S) and n(A) be
the number of elements of S and A respectively. Then the probability of event A is defined as
P (A) =
Number of cases favourable to A
n(A)
=
.
n(S)
Total number of all possible outcomes
10. Axioms of probability:
Given a finite sample space S and an event A in S, we define P (A), the probability of A, satisfies the following
three conditions.
• 0 ≤ P (A) ≤ 1
• P (S) = 1
• If A and B are mutually exclusive events, P (A ∪ B) = P (A) + P (B).
11. Probability of not happening an event A is denoted by P (A0 ) or P (A) and is defined by
P (A0 ) = 1 − P (A).
12. Let A be an event of a random experiment E, then the ratio P (A) : P (A0 ) is called the odds in favour of
A and the ratio P (A0 ) : P (A) is called the odds against A.
13. Addition rule of probability: Let S be the sample space of a random experiment E and A and B be two
events, then
P (A ∪ B) = P (A) + P (B) − P (A ∩ B).
14. If A and B are two mutually exclusive events then A ∩ B = Φ.
15. Conditional probability: Let A and B be two events connected to a random experiment E. Then the
conditional probability of the event A on the hypothesis that the event B has already occured, denoted by
P (A/B) and is defined as
P (A ∩ B)
, provided P (B) 6= 0.
P (A/B) =
P (B)
Similarly,
P (B/A) =
P (A ∩ B)
, provided P (A) 6= 0.
P (A)
16. Two events are said to be mutually independent if
P (A ∩ B) = P (A)P (B).
17. Important Note:
Independence is a property of probability but mutually exclusion is a set-theoretic property. Therefore
independent events can be identified by their probabilities and mutually exclusive events can be identified by
their events.
Department of Extension and Career Guidance
40
Department of Extension and Career Guidance
Notations: Let A and B be two events.
1. A ∪ B stands for the occurrence of A or B or both.
2. A ∩ B stands for the simultaneous occurrence of A and B.
3. A or A0 or Ac stands for non-occurrence of A
4. (A ∩ B) stands for the occurrence of only A.
5. Total probability of an event: If A1 , A2 , . . . , An are mutually exclusive and exhaustive events and B is
any event in S then
n
X
P (B) =
P (Ai ).P (B/Ai ).
i=1
P (B) is called the total probability of event B.
6. Baye’s Theorem: Suppose A1 , A2 , . . . , An are n mutually exclusive and exhaustive events such that P (Ai ) >
0 for i = 1, 2, . . . , n. Let B be any event with P (B) > 0 then
P (Ai ).P (B/Ai )
.
P (Ai /B) = P
n
P (Ai ).P (B/Ai )
i=1
Exercises
1. When three dice are rolled, number of elementary events are
(A) 23
(B) 36
(C) 63
(D) 32
2. Three coins are tossed. The probability of getting at least two heads is
(A) 3/8
(B) 7/8
(C) 1/8
(D) 1/2
3. If P (A) = 0.35, P (B) = 0.73 and P (A ∩ B) = 0.14, then P (A ∪ B) =
(A) 0.94
(B) 0.06
(C) 0.86
(D) 0.14
4. If A and B are two events such that P (A) = 0.16, P (B) = 0.24 and P (A ∩ B) = 0.11, then the probability of
obtaining only one of the two events is
(A) 0.29
(B) 0.71
(C) 0.82
(D) 0.18
5. Two events A and B are independent, then P (A/B) =
(A) P (A)
(B) P (A ∩ B)
(A)
(C) P (A) = P (B)
(D) PP (B)
6. A and B are two events such that P (A) 6= 0, P (B) 6= 0. If A and B are mutually exclusive, then
(A) P (A ∩ B) = P (A)P (B)
(B) P (A ∩ B) 6= P (A)P (B)
(C) P (A/B) = P (A)
(D) P (B/A) = P (A)
7. X speaks truth in 95 percent of cases and Y in 80 percent of cases. The percentage of cases they likely to
contradict each other in stating same fact is
(A) 14%
(B) 86%
(C) 23%
(D) 85.5%
8. A problem is given to 3 students A, B and C whose chances of solving it 1/3, 2/5 and 1/4. The probability
to solve is
(A) 4/5
(B) 3/10
(C) 7/10
(D) 1/30
9. Given P (A) = 0.50, P (B) = 0.40 and P (A ∩ B) = 0.20 then P (A/B) =
(A) 0.50
(B) 0.40
(C) 0.70
(D) 0.10
10. An urn contains 10 white and 10 black balls. While another urn contains 5 white and 10 black balls. One
urn is chosen at random and a ball is drawn from it. The probability that it is white, is
(A) 5/11
(B) 5/12
(C) 3/7
(D) 4/7
Department of Extension and Career Guidance
41
Department of Extension and Career Guidance
CHAPTER 13. PROBABILITY
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42
Chapter 14
Profit, Loss and Discount
Important Formulas
1. Profit: If the selling price (S.P.) of an article is greater than its cost price (C.P.), we say that there is a
profit.
Profit = S.P. - C.P.
2. Loss: If S.P. of an article is less than its C.P., we say that there is a loss.
Loss = C.P. - S.P.
We may list the various relations regarding profit and loss as follows :
1. In case of profit or gain (i.e., if S.P.>C.P.),
(a) Profit = S.P. - C.P.
(b) S.P. = Profit + C.P.
(c) C.P. = S.P. - Profit
Profit
(d) Profit % =
× 100
C.P.
C.P. × Profit%
(e) Profit =
100
100 + Profit%
(f) S.P. = C.P. ×
.
100
100 × S.P.
(g) C.P. =
.
100 + Profit%
2. In case of loss (i.e., if S.P.<C.P.),
(a) Loss = C.P. - S.P.
(b) S.P. = C.P. - Loss
(c) C.P. = S.P. + Loss
Loss
× 100
(d) Loss % =
C.P.
C.P. × Loss%
(e) Loss =
100
100 − Loss%
(f) S.P. = C.P. ×
.
100
43
Department of Extension and Career Guidance
(g) C.P. =
CHAPTER 14.
PROFIT, LOSS AND DISCOUNT
100 × S.P.
.
100 − Loss%
Basic Terms
1. Cost Price (CP)= The price at which you buy
2. Selling Price (SP)= The price at which you sell
3. Marked Price (MP)= The price which is mentioned
4. Profit (Profit %)=
SP −CP
CP
× 100
−SP
5. Loss (Loss %)= CPCP
× 100
6. Discount (Discount %)=
M P −SP
MP
× 100
7. Mark Up (Mark Up%)=
M P −CP
CP
× 100
8. False Weight
Profit% =
Claimed Weight − Actual Weight
× 100
Actual Weight
9. Successive Discounts
a% discount, b%discount. Effective Discount ⇒ a + b −
10. Buy x get y free
Effective Discount =
ab
100
y
× 100.
x+y
11. Special Case
Two objects are sold at the same price x
One is sold at a profit of p%, the other one at a loss of p%
Net Loss =
2p2 x
1002 − p2
Net Loss% =
12.
p2
%
100
• CP= Rs. 100
• Marked up %=10%
• Discount% = 20%
• ∴ SP = Rs. 88.
10(−20)
• 10 − 20 +
= −12%
100
exercises
1. An article was for Rs. 78,350. It’s price was
marked up by 30% and a discount of 20% was allowed on marked price. What was the profit % on
cost price?
(a) 4%
(b) 7%
(c) 5%
(d) 3%
Department of Extension and Career Guidance
(e) 7%
2. What is the difference between SI and CI on Rs.
7300 at 6% p.a. in 2 years?
(a)
(b)
(c)
(d)
(e)
Rs.
Rs.
Rs.
Rs.
Rs.
29.37
26.28
31.41
23.22
21.34
44
Department of Extension and Career Guidance
3. The SI on an amount of Rs. 22,500 at the end of
4 years is Rs. 10,800. What would be the Ci on
the same amount at the same rate at the end of 2
years?
(a) Rs. 16908
(b) Rs. 8586
(c) Rs. 5724
(d) Rs. 28224
(c)
(d)
(e)
12. (a)
(b)
(c)
(d)
(e)
(e) None of these
13. (a)
4. If P=Rs. 2000, T=2 years, R= 14% p.a., then
CI=?
Answer: CI= 14 + 14 + 14×14
100 .
5. (a)
(b)
(c)
(d)
(e)
(b)
(c)
(d)
(e)
6. (a)
(b)
14. (a)
(b)
(c)
(d)
(e)
15. (a)
(c)
(b)
(d)
(c)
(e)
(d)
7. (a)
(e)
(b)
16. (a)
(c)
(b)
(d)
(c)
(e)
(d)
8. (a)
(e)
(b)
17. (a)
(c)
(b)
(d)
(c)
(e)
(d)
(e)
9. (a)
(b)
(c)
(d)
(e)
18. (a)
(b)
(c)
(d)
(e)
10. (a)
19. (a)
(b)
(b)
(c)
(c)
(d)
(d)
(e)
(e)
11. (a)
20. (a)
(b)
(b)
Department of Extension and Career Guidance
45
Department of Extension and Career Guidance
(c)
(d)
(e)
CHAPTER 14.
PROFIT, LOSS AND DISCOUNT
(e)
25. (a)
(b)
21. (a)
(c)
(b)
(d)
(c)
(e)
(d)
(e)
26. (a)
(b)
22. (a)
(b)
(c)
(d)
(e)
23. (a)
(b)
(c)
(d)
(e)
27. (a)
(b)
(c)
(c)
(d)
(d)
(e)
(e)
28. (a)
24. (a)
(b)
(b)
(c)
(c)
(d)
(d)
(e)
Department of Extension and Career Guidance
46
Chapter 15
Sequences and Series
Important Facts and Formulas
1. Arithmetic Progression: An arithmetic progression is a list of numbers in which each term is obtained
by adding a fixed number to the preceding term except
the first term.
1. This fixed number is called the common difference
of the AP. Remember that it can be positive, negative or zero.
4. You can see that
a, a + d, a + 2d, a + 3d, . . .
represents an arithmetic progression where a is the
first term and d the common difference. This
is called the general form of an AP.
5. Formulas:
2. Let us denote the first term of an AP by a1 , second
term by a2 , . . . , nth term by an and the common
difference by d. Then the AP becomes a1 , a2 , a3 ,
. . . , an . So,
a2 − a1 = a3 − a2 = · · · = an − an−1 = d.
(a) nth term of the AP
an = a + (n − 1)d.
(b) The number of terms
n=
3. Some more examples of AP are:
l−a
+ 1.
d
(c) Sum of first n terms
(a) The heights (in cm) of some students of a
school standing in a queue in the morning assembly are 147, 148, 149, . . . , 157.
(b) The minimum temperatures (in degree celsius) recorded for a week in the month of January in a city, arranged in ascending order are
-3.1, -3.0, -2.9, -2.8, -2.7, -2.6.
Sn =
n
[2a + (n − 1)d] .
2
6. Arithmetic Mean: If a, b, c are in AP, then
b = a+b
2 and b is called the arithmetic mean of
a and c.
2. Geometric Progression: An geometric progression
(c) The balance money (in Rs.) after paying 5% is a list of numbers in which each term is obtained by
multiplying a fixed number to the preceding term except
of the total loan of Rs. 1000 every month is
the first term.
950, 900, 850, 800, . . . , 750.
You can see that
(d) The cash prizes (in Rs.) given by a school to
a, ar, ar2 , ar3 , . . .
the toppers of Classes I to XII are, respectively,
represents an geometric progression where a is the first
term and r the common ratio. This is called the gen200, 250, 300, 350, . . . , 750.
eral form of an GP.
(e) The total savings (in Rs.) after every month Formulas:
for 10 months when Rs. 50 are saved each
month are
1. nth term of the GP
50, 100, 150, 200, 250, 300, 350, 400, 450,
an = arn−1 .
500.
47
Department of Extension and Career Guidance
2. Sum of first n terms
CHAPTER 15. SEQUENCES AND SERIES
3. Sum of cubes of first n natural numbers
n
Sn =
a(r − 1)
.
r − 1)
k=n
X
k=1
3. Some Special Series:
1. Sum of first n natural numbers
k=n
X
n(n + 1)
.
2
2. Sum of squares of first n natural numbers
k=n
X
k=1
k 2 = 12 +22 +32 +· · ·+n2 =
n(n + 1)
2
2
.
4. Sum of first n odd natural numbers
k = 1 + 2 + 3 + ··· + n =
k=1
k 3 = 13 + 23 + 33 + · · · + n3 =
n(n + 1)(2n + 1)
.
6
Department of Extension and Career Guidance
k=n
X
(2k−1) = 1+3+5+7+· · · ( n terms) =
k=1
n+1
2
2
5. 1 + 3 + 5 + 7 + · · · + (2n − 1) = n2 .
48
.
Chapter 16
Ratio and Proportion
Important Facts and Formulas
1. For comparing quantities of the same type, we commonly use the method of taking difference between the
quantities.
2. In many situations, a more meaningful comparison between quantities is made by using division, i.e. by
seeing how many times one quantity is to the other quantity. This method is known as comparison by
ratio.
For example, Ishas weight is 25 kg and her fathers weight is 75 kg. We say that Ishas fathers weight and
Ishas weight are in the ratio 3 : 1.
3. For comparison by ratio, the two quantities must be in the same unit. If they are not, they should be
expressed in the same unit before the ratio is taken.
4. The same ratio may occur in different situations.
5. Note that the ratio 3 : 2 is different from 2 : 3. Thus, the order in which quantities.
6. If two ratios are equal, we say that they are in proportion and use the symbol :: or = to equate the two ratios.
(a) Example 1: We can say 3, 10, 15 and 50 are in proportion which is written as
3 : 10 :: 15 : 50 and is read as 3 is to 10 as 15 is to 50 or it is written as
3 : 10 = 15 : 50.
(b) Example 1: We can say 2, 4, 60 and 120 are in proportion which is written as
2 : 4 :: 60 : 120 and is read as 2 is to 4 as 60 is to 120.
7. If two ratios are not equal, then we say that they are not in proportion.
8. In a statement of proportion, the four quantities involved when taken in order are known as respective terms.
(a) First and fourth terms are known as extreme terms.
(b) Second and third terms are known as middle terms.
(c) Example: In 35 : 70 : : 2 : 4; 35, 70, 2, 4 are the four terms. 35 and 4 are the extreme terms. 70 and
2 are the middle terms.
exercises
1. Rs. 73689 is divided between A and B in the ratio
of 4:7. What is the difference between thrice the
share of A and twice the share of B?
(b) Rs. 46893
(c) Rs. 20097
(d) Rs. 26797
(e) Rs. 13398
(a) Rs. 36699
49
Department of Extension and Career Guidance
2. A:B=7:4. After 5 years, A:B=11:7, A=?
CHAPTER 16. RATIO AND PROPORTION
3. ?2 + 792 = 1722 − 882 − 8203.
(a) 12 years
(a) 86
(b) 14 years
(b) 89
(c) 15 years
(c) 83
(d) 28 years
(d) 93
(e) None of these
(e) None of these
exercises
1. Rs. 850 was divided among three sons Prasath,
Baskar, Chadru. If each of them had received Rs
35 less, their shares would have been in the ratio of
2:3:5. What was the amount received by Prasath?
(a) 184
(b) 174
(c) 164
(d) 154
2. Prasath divided Rs. 2500 and gave it to his three
kids A, B, C. If their shares are reduced by Rs. 5,
Rs. 10 and Rs. 15 respectively the ratio of the
remaining will be 3:4:5. Find out A’s share.
(a) 600
(b) 617.50
(c) 627
(d) 618
3. 75 kg of alloy A is mixed with 100kg of alloy B.
If alloy A has lead and tin in the ratio of 3:5 and
alloy B has tin and copper in the ratio of 2:5, then
what is the amount of tin in new alloy?
(a) 79
(b) 75
(c) 77
(d) None of these
4. The sides of a triangle are in the ratio 1/3:1/4:1/5
and its perimeter is 204 cm. What is the length of
the longest triangle?
(a) 76.8
(b) 85.8
(c) 86.8
(d) 98
5. Tin and Zinc are melted together in the ratio of
9:11. What is the weight of melted mixture if 25.5
kg of zinc has been consumed?
(a) 66.6
(b) 76.6
6. There are totally three bottles which contains milk
and water together. The ratio of the volumes of the
three bottles are 2:3:4. The mixture contains milk
and water in the ratio of 3:1,4:1, 5:1respectively. If
the contents are poured together in another bottle
then what is the price of ratio between milk and
water in the fourth bottle?
(a)
(b)
(c)
(d)
218:52
217:53
215:54
219:59
7. Two numbers are respectively 60% and 40% more
than a third number. What is the ratio between
two numbers?
(a)
(b)
(c)
(d)
7:8
9:8
8:7
6:5
8. One piece of cloth 21 meters long is to be cut into
two pieces, with the lengths of the pieces being in
a 2 : 5 ratio. What are the lengths of the pieces?
(a)
(b)
(c)
(d)
15
18
19
20
9. If 12 inches correspond to 30.48 cm, how many
number of Centimeters are there in 30 inches?
(a)
(b)
(c)
(d)
76.2
77.2
78.2
88.2
10. The sum of three numbers is 98. If the ratio of the
first to second is 2 :3 and that of the second to the
third is 5 : 8. What is the value of second number?
(a)
(b)
(c)
(d)
30
40
50
60
(c) 54.6
(d) 56.6
Department of Extension and Career Guidance
ANSWERS:
1) A 2) B 3) B 4) C 5) D 6) B 7) C 8) A 9) A 10) A
50
Chapter 17
Real Number System
Important Facts and Formulas
1. Euclids division lemma : Given positive integers a and b, there exist whole numbers q and r
satisfying a = bq + r, 0 ≤ r < b.
2. Euclids division algorithm: This is based on
Euclids division lemma. According to this, the
HCF of any two positive integers a and b, with
a > b, is obtained as follows:
Step 1: Apply the division lemma to find q and r
where a = bq + r, 0 ≤ r < b.
Step 2: If r = 0, the HCF is b. If r 6= 0, apply Euclids
lemma to b and r.
sation is unique, apart from the order in which the
prime factors occur.
4. If p is a prime and p divides a2 , then p divides a,
where a is a positive integer.
5. Let x be a rational number whose decimal expansion terminates. Then we can express x in the form
p
q , where p and q are coprime, and the prime factorisation of q is of the form 2n 5m , where n, m are
non-negative integers.
6. Let x = pq be a rational number, such that the
prime factorisation of q is of the form 2n 5m , where
n, m are non-negative integers. Then x has a decimal expression which terminates.
Step 2: Continue the process till the remainder is
zero. The divisor at this stage will be
HCF (a, b). Also, HCF(a, b) =
HCF(b, r).
3. The Fundamental Theorem of Arithmetic:
Every composite number can be expressed (factorised) as a product of primes, and this factori-
51
7. Let x = pq be a rational number, such that the
prime factorisation of q is not of the form 2n 5m ,
where n, m are non-negative integers. Then x has
a decimal expression which is non-terminating repeating (recurring).
Department of Extension and Career Guidance
CHAPTER 17. REAL NUMBER SYSTEM
Department of Extension and Career Guidance
52
Chapter 18
Simplifications
Important Facts and Formulae
BODMAS rule: This rule depicts the correct sequence in which the operations are to be executed, so as to find
out the value of a given expression.
Here B stands for Bracket, O for Of, D for Division, M for Multiplication, A for Addition and S for Subtraction.
First of all the brackets must be removed, strictly in the order () , {} , [].
After removing the brackets, we want use the following operations: 1.Of 2. Division 3. Multiplication 4.
Addition 5. Subtraction
Modulus of a real number: Modulus of a real number a is defined as:
−a, if a < 0
0,
if a = 0
|a| =
a,
if a > 0
exercises
1. (5004/139) − 6 =?
Solution:
(5004/139) − 6 = 36 − 6 = 30.
2. What mathematical operation should come at the
place of ? in the equation :
(2 ? 6 − 12/4 + 2 = 11)?
5. Along a yard 225 m long, 26 trees are planted at
equal distance, one tree being at each end of the
yard. What is the distance betweeen two consecutive trees?
Solution:
26 trees have 25 gaps betweeen them. ∴ required
distance = 225/25 = 9 m.
3. (8/88) × 8888088 =?
Solution:
(1/11) × 8888088 = 808008
6. In a garden, there are 10 rows and 12 columns of
mango trees. The distance betweeen the two tree
is 2 m and a distance of one meter is left from all
sides of the boundary of the length of the garden
is:
Solution:
Each row contains 12 plants.
Leaving 2 corner plants, 10 plants in betweeen have
10 × 2 meters and 1 meter on each side is left.
Length = 20 + 2 = 22m.
4. How many 1/8’s are there in 371/2?
Solution:
(371/2)/(1/8) = 371×8
= 300
2
7. Eight people are planning to share equally the cost
of a rental car, if one person with draws from the
arrangement and the others share equally the en-
Solution:
2 ? 6 − 12/4 + 2
=
11
2?6
=
11 + 3 − 2
2?6
=
12 ⇒? = ×.
53
Department of Extension and Career Guidance
tire cost of the car, then the share of each of the
remaining persons increased by? Solution:
Original share of one person = 1/8
New share of one person = 1/7
Increase = 1/7 1/8 = 1/56
Required fractions = (1/56)/(1/8) = 1/7
8. A piece of cloth cost Rs 35. if the length of the
piece would have been 4m longer and each meter
cost Re 1 less, the cost would have remained unchanged. how long is the piece? Solution:
Let the length of the piece be x m.
Then, cost of 1m of piece = Rs. [35/x]
35/x − 35/x + 4
=
x+4−x =
2
x + 4x − 140
=
x =
CHAPTER 18. SIMPLIFICATIONS
(c)
(d)
(e)
11. (a)
(b)
(c)
(d)
(e)
12. (a)
(b)
1
(c)
x(x + 4)/35
(d)
0
(e)
10
13. (a)
9. A man divides Rs. 8600 among 5 sons, 4 daughters and 2 nephews. If each daughter receives four
times as much as each nephew, and each son receives five as much as each nephew. how much
does each daughter receive ? Solution:
Let the share of each nephew be Rs. x.
Then, share of each daughter Rs. 4x.
Share of each son = Rs. 5x.
(b)
(c)
(d)
(e)
14. (a)
(b)
(c)
(d)
5 × 5x + 4 × 4x + 2x
=
8600
(e)
2x + 16x + 25x
=
8600
15. (a)
43x
=
8600
(b)
x
=
200
(c)
10. A man spends 2/5 of his salary on house rent, 3/10
of his salary on food, and 1/8 of his salary on conveyance. if he has Rs. 1400 left with him, find his
expenditure on food and conveyance?
Solution:
Part of the salary left
=
1 − [2/5 + 3/10 + 1/9]
=
1 − 33/40
=
7/40
(d)
(e)
16. (a)
(b)
(c)
(d)
(e)
17. (a)
(b)
Let the monthly salary be Rs. x
Then,
7/40 of x =
1400
x =
[1400 ∗ 40]/7
x =
8000
Expenditure on food = 3/10 × 8000 =Rs. 2400
Expenditure on conveyance = 1/8 × 8000 = Rs.
1000.
(c)
(d)
(e)
18. (a)
(b)
(c)
(d)
(e)
(a)
19. (a)
(b)
(b)
Department of Extension and Career Guidance
54
Department of Extension and Career Guidance
(c)
(d)
(e)
20. (a)
(b)
(e)
21. (a)
(b)
(c)
(c)
(d)
(d)
(e)
Department of Extension and Career Guidance
55
Department of Extension and Career Guidance
CHAPTER 18. SIMPLIFICATIONS
Department of Extension and Career Guidance
56
Chapter 19
Speed Calculations
Important Facts and Formulae
Note: A perfect square never ends with 2, 3, 7 or 8.
Questions:
1. Is 345712 a perfect square?.
Answer: No.
2. How many elements in the set
{2, 22, 2222, 2222, 8888, 3333}
are perfect squares?
Answer: 0.
3. How many pairs (x, y) satisfy the equation
x2 − 5y 2 = 1342.
Answer: 0.
Explanation:
Unit
Digit
of
x2
2
7
Unit
Digit
of
5y 2
0
0
Unit
Digit
of
1342
2
2
Since square of any number does not end with 2, 3, 7 or 8, unit digit of x2 must not be 2 or 7. So, this
equation does not have any solution.
4. What are the last two digits for 72008 ?
(a) 01
(b) 31
(c) 51
(d) 71
Answer: (a) 01.
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Department of Extension and Career Guidance
CHAPTER 19. SPEED CALCULATIONS
5. Is 27000001 prime or composite?
Solution:
27000001 = 27 × 106 + 1 = (3 × 102 )3 + 13 .
an + bn is always divisible by (a + b) if n is odd.
Hence, (3 × 102 )3 + 13 is divisible by 301.
∴ 27000001 is composite.
6. Is 973 prime or composite?
Solution:
973 = 103 − 33 .
an − bn is always divisible by (a − b) if n ∈ N.
Hence, 103 − 33 is divisible by 7.
∴ 973 is composite.
7. What are the last three digits for 57802 ?
(a) 219
(b) 239
(c) 249
(d) 259
Answer: (a) 01.
8. Which is greater 251501 or 501!?
Solution:
• In A.P., A.M. = (First term + Last Term)/2.
p
• G.M. = n (product of n terms).
• 501! = 501 × 500 × 499 × · · · 2 × 1.
• 1, 2, 3, . . . , 501 = A.P.
• A.M. ≥ G.M.
√
1 + 501
•
> 501 501 × 500 × 499 × · · · 2 × 1
2
√
• 251 > 501 501 × 500 × 499 × · · · 2 × 1
• 251 > 501!
9. If 2a = 3b = 4c = 5d, find a : b : c : d?
Solution:
• Close the variable and multiply all the remaining co-efficients.
•
a = 3 × 4 × 5 = 60
b = 2 × 4 × 5 = 40
c = 2 × 3 × 5 = 30
d = 2 × 3 × 4 = 24
• a : b : c : d = 60 : 40 : 30 : 24 = 30 : 20 : 15 : 12.
Department of Extension and Career Guidance
58
Chapter 20
Time and work
Important Facts and Formulae
1. If A can do a piece of work in n days, then A’s 1 day’s work =
2. If A’s i day’s work =
1
.
n
1
, then A can finish the work in n days.
n
3. If A is thrice as good a workman as B, then:
(a) Ratio of work done by A and B is 3:1.
(b) Ratio of times taken by by A and B to finish a work is 1:3.
1. If A do a piece of work in X days and B in Y days, then both of them working together will do the same
XY
work in
days.
X +Y
2. Two persons A and B, working together, can complete a piece of work in X days. If A, working alone, can
XY
complete the work in Y days, then B working alone, will complete the work in
days.
Y −X
3. If A and B, working together, can finish a piece of work in X days, B and C in Y days, C and A in Z days,
then
(a) A, B and C working together, will finish the job in
2XY Z
days.
XY + Y Z + ZX
2XY Z
days.
XY + Y Z − ZX
2XY Z
(c) B alone will finish the job in
days.
ZX + XY − Y Z
(b) A alone will finish the job in
4. If A working alone takes a days more than A and B working alone takes b days more than√
A and B together,
then the number of days taken by A and B, working together, to finish a job is given by ab.
5. If A is k times more efficient than B and is therefore able to finish a work in l days less than B, then
(a) A and B, working together, can finish the work in
kl
days.
k2 − 1
l
days.
k−1
kl
(c) B, working alone, can finish the work in
days.
k−1
(b) A, working alone, can finish the work in
59
Department of Extension and Career Guidance
Examples:
1. If 6 men and 8 boys can do a piece of work in 10
days while 26 men and 48 boys can do the same
work in 2 days, the time taken by 15 men and 20
boys in doing the same type of work will be?
Solution:
Let 1 man 1 day work = x
Let 1 boy 1 day work = y.
1
1
and 26x + 48y = .
Then 6x + 8y =
10
2
1
1
⇒ x=
and y =
.
100
200
15
20
1
⇒ 15x + 20y =
+
= .
100 200
4
∴ 15 men and 20 boys can do the work in 4 days.
2. One man, 3 women and 4 boys can do a piece of
work in 96 hours, 2 men and 8 boys can do it in 80
hours, 2 men and 3 women can do it in 120 hours.
5 men and 12 boys can do it in?
Solution:
Similar to Problem 1.
7
Answer is 43
hours.
11
3. 4 men and 6 women can complete a work in 8 days,
while 3 men and 7 women can complete it in 10
days. In how many days will 10 women complete
it?
Solution:
Similar to Problem 1.
Answer is 40 days.
4. If 12 men and 16 boys can do a piece of work in 5
days; 13 men and 24 boys can do it in 4 days, then
the ratio of the daily work done by a man to that
of a boy is?
Solution:
Let 1 man 1 day work = x
Let 1 boy 1 day work = y.
1
1
Then 12x + 16y = and 13x + 7y = .
5
4
1
1
⇒ x=
and y =
.
100
200
∴ x : y = 2 : 1.
5. 5 men and 2 boys working together can do four
times as much work as a man and a boy. Working
capacities of a woman and a boy are in the ratio:
Solution:
Let 1 man 1 day work = x
Let 1 boy 1 day work = y.
Then 5x + 2y = 4(x + y).
∴ x : y = 2 : 1.
6. 24 men can complete a work in 16 days. 32 women
can complete the same work in 24 days. 16 men
and 16 women started working and worked for 12
days. How many more men are to be added to
Department of Extension and Career Guidance
CHAPTER 20.
TIME AND WORK
complete the remaining work in 2 days?
Solution:
7. 16 men can complete a work in 12 days. 24 children
can complete the same work in 18 days. 12 men
and 8 children started working and after 8 days 3
more children joined them. How many days will
they now take to complete the remaining work?
Solution:
8. 10 women can complete a work in 7 days and 10
children take 14 days to complete the work. How
many days will 5 women and 10 children take to
complete the work?
Solution:
1
1 women 1 day work =
70
1
.
1 child 1 day work =
140
Then, 5 women and 10 children 1 day work
1
1
1
=5 + 10
= .
70
140
7
∴ 5 women and 10 children will complete the work
in 7 days.
9. 12 children take 16 days to complete a work which
can be completed by eight adults in 12 days. 16
adults started working and 3 days 10 adults left
and 4 children joined them. How many days will
they take to complete the remaining work?
Solution:
1
.
1 child 1 day work =
192
1
1 adult 1 day work =
.
96
1
1
Workdone in 3 days =
× 16 × 3 = .
96
2
1
1
∴ Remaining work = 1 − = .
2
2
6
4
1
= .
6 adults and 4 children 1 day work = +
96 192
2
1
work is done by them in 1 day.
12
1
1
work is done by them = 12 × = 6 days.
2
2
10. 12 men can complete a piece of work in 4 days,
while 15 men can complete the same work in 4
days. 6 men start working on the job and after
working for 2 days, all of them stopped working.
How many women should be put on the job to
complete the remaining work, if it is to be completed in 3 days?
Solution:
60
Department of Extension and Career Guidance
Similar to Problem 9.
Answer is 15 women.
10. 45 men can complete a work in 16 days. Six
days after they started working, 30 more
men joined them. How many days will they
now take to complete the remaining work?
Questions:
Answers:
4
4
1. Worker A takes 8 hours to do a job. Worker 4 9 , 6, 3,(16,48,28 5 ,144), 27, 7.5, 30, Rs.75, 10.25,
B takes 10 hours to do the same job. How 6.
long should it take both A and B, working
together but independently, to do the same Exercise:
job?
1. A does a work in days and B does the same
work in 15 days. In how many days they
2. A and B together can complete a piece of
together will do the same work?
work in 4 days. If A alone can complete the
(A) 5 days
(B) 6 days
same work in 12 days, in how many days can
(C) 8 days
(D) 9 days
B alone complete that work?
2. P can complete a work in 12 days working 8
3. A can do a piece of work in 7 days of 9
hours a day. Q can complete the same work
hours each and B can do it in 6 days of 7
in 8 days working 10 hours a day. If both
hours each. How long will they take to do
P and Q work together, working 8 hours a
it, working together 8 25 hours a day?
day, in how many days can they complete
the work?
4. A and B can do a piece of work in 18 days;
6
5
days
(B) 5 11
days
(A) 5 11
B and C each do it in 24 days; A and C
5
6
(C) 6 11 days
(D) 6 11
days
can do it in 36 days. In how many days will
A, B and C finish it, working together and
3. A and B can do a work in 8 days, B and C
separately?
can do the same work in 12 days. A, B, and
C together can finish it in 6 days. A nd C
5. A is twice as good a workman as B and totogether will do it it
gether they finish a piece of work in 18 days.
(A) 4 days
(B) 6 days
In how many days will A alone finish the
(C) 8 days
(D) 12 days
work?
4. A can finish a work in 18 days and B can
6. A can do a certain job in 12 days. B is 60%
do the same work in 15 days. B worked
more efficient than A. How many days does
for 10 days and left the job. In how many
B alone take to do the same job?
days, A alone can finish the remaining work?
(A 5 days
(B) 5 12 days
7. A can do a piece of work in 80 days. He
(C) 6 days
(D) 8 days
works at it for 10 days and then B alone finishes the remaining work in 42 days. In how
5. A and B can do a work in 20 days and 12
much time will A and B, working together,
days respectively. A started the work alone
finish the work?
and then after 4 days Y joined him till the
completion of the work. How long did the
8. A and B undertake to do a piece of work for
work last?
Rs. 600. A alone can do it in 6 days while
(A) 6 days
(B) 10 days
B alone can do it in 8 days. With the help
(C) 15 days
(D) 20 days
of C, they finish it in 3 days. Find the share
6. A and B can complete a work in 12
of each.
days.
A alone can complete it in 20
9. A and B working separately can do a piece
days. If B does the work only for half
of work in 9 and 12 days respectively. If
a day daily, then in how many days A
they work for a day alternatively, A beginand B together will complete the work?
ning, in how many days, the work will be
(A) 10 days
(B) 11 days
completed?
(C) 15 days
(D) 20 days
exercises
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61
Department of Extension and Career Guidance
1. 24 boys will complete a piece of work in 18 days.
2 days after they started the work, 8 more boys
joined with them. In how many days will all of
them together finish the leftover work?
(a) 11 days
(b) 12 days
(c) 15 days
(d) 17 days
2. A team of friends planned to finish a construction
work in 60 days. Out of them, 5 friends couldnt
come and the job was finished in 80 days. What
was the total number of friends in the starting?
(a) 40 friends
(b) 17 friends
(c) 27 friends
(d) 20 friends
3. 18 boys will finish the construction of a wall in 36
days. How many days will 12 boys take to complete the same wall?
(a) 18 days
(b) 10 days
(c) 15 days
(d) 14 days
4. X works 6 hours for 9 days and 5 hours on 10th day.
Find Xs earnings at the rate of Rs.60 per hour.
(a) Rs. 5403
(b) Rs. 2341
(c) Rs. 3540
(d) Rs. 3347
5. Sixteen boys and 12 girls will complete a work in
30 days. 18 girls can complete the same piece of
work in 60 days. In how many days can 12 boys
and 27 girls complete the same work?
CHAPTER 20.
TIME AND WORK
(a) 48 men
(b) 38 men
(c) 22 men
(d) 32 men
7. X will do a piece of work in 36 days. Where as X
and Y together can do the same work in 24 days.
If Y has to do the work alone, how many days will
take to finish it?
(a) 72 days
(b) 50 days
(c) 63 days
(d) 30 days
8. 6 boys working 5 hours a day to bind 1500 Notes
in 8 days. At the same amount of binding notes.
In what period of time can 4 boys bind 1600 Notes
for working 8 hours a day?
(a) 7 days
(b) 8 days
(c) 11 days
(d) 14 days
9. 5 girls can do a piece of work in 5 days. 8 boys can
finish it in 4 days. In how many days will 8 boys
and 10 girls finish it?
(a) 2 days
(b) 5 days
7
days
(c) 1
13
5
days
(d) 2
11
10. 14 girls take 16 days to finish a work. 8 girls started
working and after 12 days, 8 more than joined together with them. How many days will they take
to finish the leftmore work?
(a) 25 days
(a) 9 days
(b) 12 days
(b) 12 days
(c) 14 days
(c) 13 days
(d) 24 days
(d) 15 days
6. If 16 men can search 6(2/3) m tunel in one day.
How many men will be needed to search 20 m long Answers:
1)B 2)D 3)A 4)C 5)D 6)A 7)A 8)B 9)C 10)D
tunel?
Department of Extension and Career Guidance
62
Chapter 21
Time, Speed & Distance
Important Facts and Formulae
1. Speed of the object =
Distance covered by the object
Time taken to cover the distance
2. Formulae:
Speed = Distance
Time
Time = Distance
Speed
Distance = Speed × Time
1
T
⇒
If D is constant, s ∝
⇒
If T is constant, D ∝ s
⇒
If s is constant, D ∝ T
3. Units of Measurement:
(a) Time → Second (s), Minutes (min), Hours (h)
(b) Distance → Metres (m), Kilometres (km), Miles
(c) Speed → mps, kmph, mph.
4. Conversion of Units:
(a) 1 hour = 60 min = 60× 60 sec = 3600 sec
(b) 1 km = 1000 m = 0.6214 miles
(c) 1 mile = 1.609 km ⇒ 8 km = 5 miles
(d) 1 yard = 3 feet, 1 feet = 12 inch
(e) 1 kmph 5/18 mps, 1 kmph = 5/8 miles per hour
5. Concept: If a man changes his speed in the ratio m : n, the ratio of times taken becomes n : m.
6. Q1.: Walking 5/6 of his usual rate, a boy reaches his school 12 min late. Find the usual time to reach the
school.
Answer:
Speed = 5/6 usual speed
Time = 6/5 usual time
5
1
6
5T = 5T + 5T
1
So, 5 T = 12 min ⇒ T = 12 × 5 = 60 min.
7. Q2.: Walking at 13/11 of her usual rate, a girl takes 3 min less to reach her school. Find the usual time to
reach the school.
Answer:
Speed = 13/11 usual speed
Time = 11/13 usual time
11
13
2
13 T = 13 T − 13 T
2
So, 13 T = 3 min ⇒ T = 3×13
= 19.50 min.
2
8. Average speed=
2uv
u+v
=
3uvw
uv+vw+wu .
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Department of Extension and Career Guidance
CHAPTER 21. TIME, SPEED & DISTANCE
9. Concept: If two persons start at the same time from two points A and B towards each other and after
crossing they take x and y hours in reaching B and A respectively, then
r
Speed of first
y
=
.
Speed of second
x
10. Q2.: A man starts from B to K and another from K to B at the same time. After passing each other, they
complete their journeys in 3 13 and 4 54 hours respectively. If the speed of the first is 12 kmph, find the speed
of the second man.
Answer:
s
4 54
6
Speed of first
= .
=
1
Speed of second
5
33
⇒
12
S2
=
6
5
⇒ S2 = 10 kmph.
11. Concept: If a boy moves at an average speed of V1 kmph to cover a distance of D km without stopping and
moves at an average speed of V2 kmph to cover the same distance with stoppages, then
Stoppage time per hour =
V1 − V2
.
V1
12. Q3. A train travels at a speed of 60 kmph between two stations 240 km apart, without stopping. It goes at
an average speed of 40 kmph when it stops. What is the average stoppage time per hour?
Answer:
At 60 kmph, 240 km ⇒ Time = 4 hours
At 40 kmph, 240 km ⇒ Time = 6 hours
Stoppage time = 2 hours ⇒ Stoppage time per hour = 26 = 31 hour.
2
Using Formula V1V−V
= 60 − 4060 = 31 .
1
Application of LCM in TSD
1.
ST
=1
D
2. Example 1:
• 10 kmph → 20 min late.
• 20 kmph → 10 min early.
• D =?
Answer:
• D = Constant i.e., fixed quantity.
• LCM(10,20)=20 km → 2 hr
1 hr
• 20 km → 60 minutes
• 10 km → 30 minutes
3. Example 2:
• 9 kmph → 43 min late.
• 36 kmph → 17 min early.
• D =?
Answer:
• D = Constant i.e., fixed quantity.
• LCM(9,36)=36 km → 4 hr
1 hr
• 36 km → 180 minutes
• 12 km → 60 minutes
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Department of Extension and Career Guidance
4. Example 3:
• 20 kmph → 40 min late.
• 30 kmph → 10 min late.
• D =?
Answer:
• D = Constant i.e., fixed quantity.
• LCM(20,30)=60 km → 3 hr
2 hr
• 60 km → 60 minutes
• 30 km → 30 minutes
Quick Questions
1. What is the length of a bridge, which a man riding at 15 kmph can cross in 5 min?
2. Mukesh walks 10 km in 5 hours. How much time will take to travel 28 km?
3. If a cyclist covers 11 km in 3 hours, find the distance covered in 5 hours.
4. A man walks at 5 kmph for 6 hours and at 4 kmph for 12 hours. Find the average speed.
5. Walking 3/4-th of his usual rate, a man is 1.5 hour late. Find the usual time.
6. What is the ratio of speeds of two trains one travelling at 45 kmph and another at 10 m/s?
7. In a minute how many poles will a railway passenger pass by if they are spaced 50 m apart and the train’s
speed is 60 kmph?
8. A 200 m long train is moving at 60 kmph. How long will it take to pass a pole?
9. A 180 m long train is moving at 54 kmph. How long will it take to pass pass a tunnel 720 m long?
10. A train running at 30 mps takes 30 sec to cross a platform 600 m long. What is the length the train?
Exercises
1. Ramesh travels 600 km to reach home partly by train and by car. He takes 8 hours if he travels 120 km by
train and the rest by car. But he would take 20 min more if he travels 200 km by train and the rest by car.
Find the Speeds of the train and car.
(1) 30 kmph, 40 kmph
(2) 60 kmph, 80 kmph
(3) 15 kmph, 60 kmph
(4) None of these
2. Excluding stoppages, the speed of a mobike is 63 kmph & including stoppages it is 36 kmph. The number of
minutes per hour for which the mobike stops is
(1) 25.71
(2) 26.71
(3) 27.71
(4) 28.71
3. A student walks to school at the rate of 2.5 kmph and reaches 6 min too late. Next dat he increases his speed
by 2 kmph and then reaches school 10 min early. The distance of the school from his home is
(1) 1.5 km
(2) 3 km
(3) 6 km
(4) 12 km
4. A cyclist starts from Delhi towards Gurgaon which is 100 km away. He is able to maintain a speed of 20
kmph in the first hour, after which his speed falls to 18 kmph. He is able to maintain this speed for the next
hour after which it fall to 16.2 kmph, which also he maintains for an hour. In the fourth hour he is able to
maintain a speed 14.58 kmph and so on. How much time, approximately does he take to reach Gurgaon?
(1) 6 hrs 21 min
(2) 6 hrs 36 min
(3) 6 hrs 51 min
(4) 6 hrs 12 min
5. A and B start at the same time from L and M to go to M and L, a distance of 42 km at the rates of 4 kmph
and 3 kmph respectively. They meet at N, then go to M and L and return immediately and meet again at
D. Find the distance DN.
(1) 6 km
(2) 12 km
(3) 18 km
(4) 24 km
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Department of Extension and Career Guidance
CHAPTER 21. TIME, SPEED & DISTANCE
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66
Chapter 22
Average
Important Facts and Formulae
There are train based problems based on two object, First is Train and second object is that which is crossed
by the train.
1. If a train moving or cross a pole or man then the first object is train and the second object is pole or man.
2. If a train moving or cross the platform then the first object is train and the second object is platform which
is train cross.
3. If a train moving or cross a man who is standing on platform then the first object is train and the second
object is man.
4. When A train is crossing or moving another train in the same direction of opposite direction than the first
object is first train and the second object is second train.
examples
1. A passenger train 330 m long which is running at a speed of 60 kmph. In what time will it pass a man who
is running at a speed 6 kmph in the opposite direction in which the train is moving?
Answer: Steps:
(a) If direction is given in the opposite direction, then we add both speeds that relative speed = 60 + 6 =
66 kmph.
(b) Now, convert in into mps using 66 × 5/18 = 55/3 mps.
(c) If the train time taken to passing a man who running in opposite direction, that is 55/3 mps. So we can
easily get the distance of mps so it cover 330 m that is = 330 × 3/55 = 18 sec.
2. Two superfast train 180 m and 180 m in length respectively are running in opposite direction, one at the
rate of 58 km and the other at the rate of 50 km an hour. What time will they completely clear each of ither
from the moment they meet?
Answer: Steps:
(a) Two superfast trains are running in opposite direction and their relative speed is 58 + 50 =108 kmph
= 108 × 5/18 = 30 mps.
(b) Required time = Total length / Relative speed = 360/30=12 sec.
67
Department of Extension and Career Guidance
CHAPTER 22. AVERAGE
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68
Chapter 23
Bank Discount
Important Facts and Formulas
Banker’s Discount: Suppose a merchant A buys goods worth, say Rs. 10,000 from another merchant B at a
credit of say 5 months. Then, B prepares a bill, called the bill of exchange. A signs this bill and allows B to
withdraw the amount from his bank account after 5 months.
The date exactly after 5 months is called nominally due date. Three days (known as grace days) are added
to it to get a date, known as legally due date.
Suppose B wants to have the money before the legally due date. Then he can have the money from the banker
or a brker, who deducts S.I on the face value (i.e., Rs. 10,000 in this case) for the period from the date on which the
bill was discounted (i.e., paid by the banker) and legally due date. This amount is known as Banker’s Discount
(B.D.).
Banker’s Gain = B.D. - T.D. for the unexpired time.
Note: When the date of the bill is not given, grace days are not to be added.
important formulae
1. B.D. = S.I. on the bill for unexpired time.
2. B.G. = B.D. - T.D. = S.I. on T.D. =
3. T.D. =
√
(T.D.)2
.
P.W.
P.W. × B.G..
4. B.D. =
Amount × Rate × Time
.
100
5. T.D. =
Amount × Rate × Time
.
100 + (Rate × Time)
6. T.D. =
B.D. × T.D
B.D. − T.D.
7. T.D. =
B.G. × 100
Rate × Time
69
Department of Extension and Career Guidance
Department of Extension and Career Guidance
CHAPTER 23.
BANK DISCOUNT
70
Chapter 24
True Discount
Important Facts and Formulas
Suppose a man has to pay Rs. 156 after 4 years and the rate of interest is 14% per annum. Clearly, Rs. 100 at
14% will amount to Rs. 156 in 4 years. So the payment of Rs. 100 now will clear off the debt of Rs. 156 due 4
years hence. We say that:
Sum due = Rs. 156 due 4 years hence;
Present Worth (P.W.) = Rs. 100;
True Discount (T.D.) = Rs. (156-100) = Rs. 56 = Sum due - P.W.
We define:
T.D.
Amount
=
=
Interest on P.W.
P.W. + T.D.
Interest is reckoned on P.W. and the true discount is reckoned on the amount.
important formulae
Let rate = R% per annum and Time = T years. Then,
1. P.W. =
100 × T.D.
100 × Amount
=
100 + (R × T )
R×T
2. Sum =
S.I. × T.D.
S.I. − T.D.
3. When the sum is put at compound interest, then P.W. = 71
Amount
T .
R
1+
100
Department of Extension and Career Guidance
CHAPTER 24. TRUE DISCOUNT
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72
Chapter 25
Website Model Question Papers
Collection
Model Question Paper - 1
1. If the area of the triangle BCD is 8, what is the
area of the square ABCD?
(a) 16
(b) 82
(c) 8
(d) 4
(e) mx + ny
5. A labourer is paid Rs. 8 per hour for an 8 hour day
and 1.5 times that rate for each hour in excess of 8
hours in a single day. If the labourer received Rs.
80 for a single day’s work, how long did he work
on that day?
(a) 6 hours 40 minutes
(e) 22
(b) 9 hours 20 minutes
2. A boy receives grades of 91, 88, 86 and 78 in four
of his major subjects. what must he receive in his
fifth major subject in order to average 85?
(a) 86
(b) 85
(c) 84
(d) 83
(e) 82
3. John has more money than Sam but less than Bill.
If the amount held by John, Sam and Bill are x, y
and z respectively, which of the following is true?
(c) 9 hours 30 minutes
(d) 9 hours 40 minutes
(e) 10 hours
6. In the same amount of time a new production assembly robot can assemble 8 times as many transmissions as an old assembly line. If the new robot
can assemble x transmissions per hour, how many
transmissions can the new robot and the old assembly line produce together in five days of round
the clock production.
(c) y < x < z
45x
8
(b) 15x
135x
(c)
8
(d) 135x
(d) y < z < x
(e) 1080x
(a) z < x < y
(b) x < z < y
(e) x < y < z
(a)
7. If Sasi has Rs. 5 more than Tarun and if Tarun
has Rs. 2 more than Eswar, which of the following
exchanges will ensure that each of the three has an
equal amount of money?
4. If mx+ny = 12my and my 6= 0, then x/y+n/m =?
(a) 12
(b) 12mn
(a) Sasi must give Eswar Rs. 3 and Tarun Rs. 1
(c) 12m + 12y
(b) Tarun must give Sasi Rs. 4 and Sasi must
give Eswar Rs. 5
(d) 0
73
Department of Extension and Career
CHAPTER
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25. WEBSITE MODEL QUESTION PAPERS COLLECTION
(c) Eswar must give Sasi Rs. 1 and Sasi must
give Tarun Ra. 1.
(d) Sasi must give Eswar Rs. 4 and Tarun must
give Eswar Rs. 5
(e) Either Sasi or Eswar must give Tarun Rs. 7.
8. Ravi is standing 180 meters due north of point P.
Latha is standing 240 meters due west of point P.
What is the shortest distance between Ravi and
Latha?
(a) 60 meters
(b) 300 meters
(c) 420 meters
(d) 900 meters
(e) 9000 meters
√
√
9. (4 + 5)(4 − 5) is equal to
(a) -1
(b) 0
(c) 11
(d) 21
√
(e) 11 + 8 5
10. If interest on a savings account is paid monthly
at an annual rate of 6.25% and if the interest is
not reinvested, then in how many years will the
total amount of interest earned equal the amount
of money saved in the account?
(a) 36
(b) 24
(c) 18
(d) 16
(e) 12
11. If hose A can fill up a tank in 20 minutes and hose
B can fill up the same tank in 15 minutes, how
long will it take for the hoses together to fill up
the tank?
(a) 5 minutes
(b) 15/2 minutes
(c) 60/7 minutes
(d) 65/7 minutes
(e) 12 minutes
12. John rents a car for d days. He pays Rs. m per
day for each of the first 7 days, and half that rate
for each additional day. Find the total charge if
d > 7.
(a) m + 2m(d − 7)
(b) m + m/2(d − 7)
(c) 7m + m/2(d − 7)
Department of Extension and Career Guidance
(d) 7m + md/2
(e) 7m + 2md
13. The net price of a certain article is Rs. 306 after successive discounts of 15% and 10% off the
marked price. What is the marked price?
(a)
(b)
(c)
(d)
(e)
Rs. 234.09
Rs. 400
Rs. 382.50
Rs. 408
None of these
14. A school has enough bread to feed 30 children for
4 days. If 10 more children are added, how many
days will the bread last?
(a)
(b)
(c)
(d)
(e)
16/3
4/3
8/3
12
3
15. A train 100 metres long running at a speed of 50
km/hr crosses a 120 m. long train coming from the
opposite direction in 6 seconds. What is the speed
of the other train?
(a)
(b)
(c)
(d)
(e)
82
70
85
72
65
kmph
kmph
kmph
kmph
kmph
16. The numbers 34041 and 32506 when divided by a
certain number of three digits, leave the same remainder. What is the number?
(a)
(b)
(c)
(d)
(e)
535
405
357
307
275
17. A student was asked to find the arithmetic mean
of the numbers 3, 11, 7, 9, 15, 13, 8, 19, 17, 21, 14
and x. He found the mean to be 12. What should
be the number in the place of x?
(a)
(b)
(c)
(d)
(e)
3
7
17
31
None of these
18. 10 years ago, the average age of a family of 4 members was 24 years. Tow children having been born
(with age difference of 2 years), the present average age of the family is the same. The present age
of the youngest child is:
74
Department of Extension and Career Guidance
(a) 1 year
22. A man wants to reach a window which is 40 feet
above the ground. The distance from the foot of
the ladder to the wall is 9 feet. How long should
the ladder be?
(b) 2 years
(c) 3 years
(d) 4 years
(a) 41
(e) 5 years
(b) 49
19. January 1, 1995 was a Sunday, what day of the
week lies on January 1, 1996?
(c) 31
(d) 39
(e) Data inadequate
(a) Monday
(b) Tuesday
23. 2 =5 ; 4 = 18 ; 6 = 39 ; 8 = 68 ; 10 = ?
(c) Friday
(a) 100
(d) Thursday
(b) 105
(e) Sunday
(c) 115
20. The price of 438 oranges is Rs.1384.08. What will
be the approximate price of 8 dozen of oranges?
(a) 388
(d) 120
(e) 125
24. In the series POQ, SRT, VUW,?
(b) 300
(a) XYZ
(c) 300.45
(b) XZY
(d) 384
(c) YXZ
(e) None of these
(d) YZX
21. If 10 be added to 4 times a certain number, the
result in 5 less than five times the number . The
number is
(e) None of these
25. Which number is wrong in the given series? 1236,
2346, 3456, 4566, 5686
(a) 15
(a) 5686
(b) 20
(b) 1236
(c) 30
(c) 3456
(d) 5/3
(d) 4566
(e) Data inadequate
(e) None of these
Model Question Paper - 2
1. Every letter in the alphabet has number value
which is equal to its place in the alphabet; the
letter A has a value of 1 and C a value of 3. The
number value of a word is obtained by adding up
the values of the letters in the word and then multiplying that sum by the length of the word. The
word ’DFGH’ would have a number value of
(a) 25
(b) 44
(c) 66
(a) b
(b) −b
(c) a − b
(d) −a − b
3. The average monthly income of P and Q is Rs.
5050. The average monthly income of Q and R is
Rs. 6250 and the average monthly income of P and
R is Rs. 5200. The monthly income of P is:
(a) 3500
(b) 4000
(d) 100
(c) 4050
(e) 108
(d) 5000
2. If ab > 0 and a < 0, which of the following is
negative?
Department of Extension and Career Guidance
4. A library has an average of 510 visitors on Sundays and 240 on other days. The average number
75
Department of Extension and Career
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25. WEBSITE MODEL QUESTION PAPERS COLLECTION
of visitors per day in a month of 30 days beginning
with a Sunday is:
(a) 250
(b) 276
(c) 280
(d) 285
5. The sum of two number is 25 and their difference
is 13. Find their product.
(a) 104
(b) 114
10. A sum fetched a total simple interest of Rs.
4016.25 at the rate of 9% p.a. in 5 years. What is
the sum?
(a) Rs. 4462.50
(b) Rs. 8032.50
(c) Rs. 8900
(d) Rs. 8925
11. A person takes a loan of Rs. 200 at 5% simple interest. He returns Rs. 100 at the end of 1 year.
In order to clear his dues at the end of 2 years, he
would pay:
(c) 315
(a) Rs. 105
(d) 325
(b) Rs. 110
6. What is the number?
(I) The sum of the two digits is 8. The ratio of
the two digits is 1 : 3.
(II) The product of the two digit of a number is
12. The quotient of two digits is 3.
(c) Rs. 115
(d) Rs. 115.50
12. The difference between the length and breadth of
a rectangle is 23 m. If its perimeter is 206 m, then
its area is:
(a) 1520 m2
(a) I alone sufficient while II alone not sufficient
to answer
(b) 2420 m2
(b) II alone sufficient while I alone not sufficient
to answer
(d) 2520 m2
(c) Either I or II alone sufficient to answer
(c) 2480 m2
13. What was the day of the week on 28th May, 2006?
(d) Both I and II are not sufficient to answer
(a) Friday
(e) Both I and II are necessary to answer
(b) Saturday
7. A is two years older than B who is twice as old as
C. If the total of the ages of A, B and C be 27, the
how old is B?
(a) 7
(c) Sunday
(d) Monday
14. If 10 be added to 4 times a certain number, the
result is 5 less than five times the number . The
number is
(b) 8
(c) 9
(d) 10
8. 173.5 × 17? = 178 .
(a) 2.29
(b) 2.75
(c) 4.25
(d) 4.5
4
9. A and B together have Rs. 1210. If
of A’s
15
2
amount is equal to
of B’s amount, how much
5
amount does B have?
(a) Rs. 460
(a) 15
(b) 20
(c) 30
5
(d)
3
15. A man wants to reach a window which is 40 feet
above the ground. The distance from the foot of
the ladder to the wall is 9 feet. How long should
the ladder be?
(a) 41
(b) 49
(c) 31
(d) 39
16. 2 =5 ; 4 = 18 ; 6 = 39 ; 8 = 68 ; 10 = ?
(b) Rs. 484
(a) 100
(c) Rs. 550
(b) 105
(d) Rs. 664
(c) 115
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76
Department of Extension and Career Guidance
(d) 120
(c) Rs. 76,375
(d) Rs. 81,250
17. In the series POQ, SRT, VUW,?
22. Shyam travels 7 km to the north. Then again he
turns to the right and walks 3 km. Then again he
turns to his right moves 7 km forward. How may
kilometers away is he from the starting point?
(a) XYZ
(b) XZY
(c) YXZ
(d) YZX
(a) 10 km
18. In how many ways can a group of 5 men and 2
women be made out of a total of 7 men and 3
women?
(b) 3 km
(c) 20 km
(d) 6 km
(a) 63
23. A and B can do a piece of work in 18 days, B and
C in 24 days; A and C in 36 days. In what time
can they do it all working together?
(b) 90
(c) 126
(d) 45
(a) 12 days
(e) 135
(b) 13 days
19. Find out the wrong number in the given sequence
of numbers. 8, 13, 21, 32, 47, 63, 83
(c) 16 days
(d) 26 days
(a) 47
24. A train covers a distance of 80 km at a speed of
40 km/hr for the first 60 km and the remaining
distance at the speed of 20 km/hr. What is the
average speed of the train on the journey?
(b) 63
(c) 32
(d) 83
20. 1, 4, 9, 16, 25, 36, 49, (....)
(a) 32 kmph
(a) 54
(b) 30 kmph
(b) 56
(c) 25 kmph
(c) 64
(d) None of these
(d) 81
21. The price of a car is Rs. 3,25,000. It was insured
to 85% of its price. The car was damaged completely in an accident and the insurance company
paid 90% of the insurance what was the difference
between the price of the car and the amount received?
25. Alfred buys an old scooter for Rs. 4700 and spends
Rs.800 on its repairs. If he sells the scooter for Rs.
5800, his gain percent is
(a) Rs. 32,000
4
(a) 4 %
7
5
(b) 5 %
11
(c) 10%
(b) Rs. 48,750
(d) 12%
Model Question Paper - 3
1. Find the value of x
1
1
8.5 − 5 − 7 + 2.8/x
× 4.25/(0.2)2 = 306.
2
2
(a)
150
11
(b)
177
110
(c)
170
11
(d)
17
110
(a) 4.5
(b) 5.5
(c) 3.5
(d) 6.5
√
0.289
2. Simplify: √
0.00121
Department of Extension and Career Guidance
Answer: (c)
77
Department of Extension and Career
CHAPTER
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25. WEBSITE MODEL QUESTION PAPERS COLLECTION
√
0.289
√
0.00121
• Let Marked up% = x.
20x
45 × 5
• x − 20 −
= 25 ⇒ x =
.
100
4
45 × 5
• M.P. = 1200 + 1200 ×
= 1875.
4 × 100
r
=
=
289 100000
×
121
1000
17
170
× 10 =
.
11
11
3. The average of ten number is multiplied by 12, then
the average of the new set of number is
(a) 7
7. 10 men and 15 women together can complete a
work in 6 days. It takes 100 days for one man
alone to complete the same work. How many days
will be required for one woman alone to complete
the same work?
(b) 19
(a) 90
(c) 82
(b) 125
(d) 84
(c) 145
4. If 15% of 40 is greater than 25% of a number by 2,
then the number is
(a) 12
(b) 16
(d) None of these.
8. The compound interest on a sum for 2 years at
10% per annum is Rs. 525. The simple interest on
the same sum for double the time at half the rate
per cent per annum is
(c) 24
(a) Rs. 400
(d) 32
(b) Rs. 500
(c) Rs. 600
Answer: (b)
(d) Rs. 800
25
15
× 40 −
×x
100
100
1
6− ×x
4
1
×x
4
x
9. Two trains of equal length are running on parallel lines in the same direction at 46 kmph and 36
kmph. The faster train passes the slower train in
36 seconds. The length of each train is
=
2
=
2
=
6−2
(a) 50 m
=
16
(b) 72 m
(c) 80 m
5. If the price of a book is first decreased by 25% and
then increased by 20% then the net change in the
price will be
(a) no change
(b) 5% increase
(c) 5% decrease
(d) 10% decrease
Answer: (d)
(−25)(20)
−25 + 20 +
= −5 − 5 = −10
100
6. At what price should a shopkeeper mark a radio
that cost him Rs. 1200 in order that he may offer
a discount of 20% on the marked price and still
make a profit of 25%?
(a) Rs. 1675
(b) Rs. 1875
(c) Rs. 1900
(d) Rs. 2025
Answer: (b)
Department of Extension and Career Guidance
(d) 82 m
1 1 1
+ + = 4, then x =?
3 2 x
5
(a)
18
6
(b)
19
18
(c)
5
24
(d)
11
10. If
Answer: (b)
1 1 1
+ +
3 2 x
1
x
1
x
1
x
=
4
=
4−
=
=
∴ x =
1 1
−
3 2
24 − 2 − 3
6
19
6
6
19
78
Department of Extension and Career Guidance
11. 7 is added to a certain number, the sum is multiplied by 5, the product is divided by 9 and 3 is
subtracted from the quotient. The remainder left
is 12. The number is
(a) 20
(b) 30
(c) 40
(d) 60
12. There are two examination rooms A and B. If 10
students are sent from A to B, then the number of
students in each room is the same. If 20 candidates
are sent from B to A, then the number of students
in A is double the number of students in B. The
number of students in room A is ?
(a) 20
(b) 80
(c) 100
(d) 12
13. What least number must be subtracted from
734689 to make it divisible by 3?
(a) 3
(b) 1
(c) 6
(d) 4
14. Find the nearest number to 5028, which is exactly
divisible by 64.
(a) 5052
(b) 5054
(c) 5056
(d) 5058
15. Three years ago the average age of a five member
family was 17 years. A baby having been born the
average is now 17 years. Find the age of the baby?
(a) 1 year
(b) 2 years
(c) 3 years
(d) None of these
16. The average age of a group of 16 persons is 28 years
3 months. Two persons each 58 years old left the
group. The average age of the remaining persons
is
(a) 24
(b) 28
(c) 22
(d) None of these
Department of Extension and Career Guidance
17. Two persons travel certain distance at the speed
of 3.75 km / hr and 3 km/hr. First person reaches
the destination half an hour earlier find the distance traveled.
(a)
(b)
(c)
(d)
7.5 km
7.8 km
8 km
9 km
18. The distance between two stations A and B is 220
km. A train leaves the station A with a speed of
80 km/hr. After half an hour another train departs from the station B with a speed of 100 km
per hour. The distance from the station A of the
point where both the trains meet is
(a)
(b)
(c)
(d)
100 km
120 km
110 km
80 km
19. C’s mother was four times as old as C ten years
ago. After 10 years she will be twice as old as C.
how old is C now?
(a)
(b)
(c)
(d)
50
30
20
None of these
20. Five boys are sitting in a row. A is on the left of
D and to the right of B. E is on the left of B but
to the right of C. Who sits on the extremes?
(a)
(b)
(c)
(d)
C and D
A and B
D and E
C and E
(Directions for questions 21 – 22): Each problem consists of three statements. Based on the first
two statements, the third statement may be true,
false, or uncertain.
21. Tanya is older than Eric.
Cliff is older than Tanya.
Eric is older than Cliff.
If the first two statements are true, the third statement is
(a) True
(b) False
(c) Uncertain
22. All the tulips in Zoe’s garden are white. All the
pansies in Zoe’s garden are yellow. All the flowers
in Zoe’s garden are either white or yellow
If the first two statements are true, the third statement is
(a) True
79
Department of Extension and Career
CHAPTER
Guidance
25. WEBSITE MODEL QUESTION PAPERS COLLECTION
(b) False
(b) Friday
(c) Uncertain
(c) Saturday
23. Which letter replaces the question mark?
(d) Sunday
25. Look at this series:
Figure
2, 1, (1/2), (1/4), ...
(a) P
(b) S
What number should come next?
(c) Data inadequate
(a) (1/3)
(d) Q
(b) (1/8)
24. What was the day of the week on 28th May, 2006?
(c) (2/8)
(d) (1/16)
(a) Thursday
Model Question Paper - 4
1. 8, 7, 11, 12, 14, 17, 17, 22, (....)
(a) 27
(b) 20
(c) 22
(d) 24
2. 2. A man wants to sell his scooter. There are two
offers, one at Rs. 12,000 cash and the other a credit
of Rs. 12,880 to be paid after 8 months, money being at 18% per annum. Which is the better offer?
(a) Rs. 12,000 in cash
(b) 10
(c) 17
(d) 20
6. Ayesha’s father was 38 years of age when she was
born while her mother was 36 years old when her
brother four years younger to her was born. What
is the difference between the ages of her parents?
(a) 2 years
(b) 4 years
(c) 6 years
(d) 8 years
(b) Rs. 12,880 in credit
(c) Both are equal
(d) Nil
√
14
625
11
3.
×√ ×√
is equal to
11
25
196
(a) 5
(b) 6
(c) 8
7. In an election between two candidates, one got 55%
of the total valid votes, 20% of the votes were invalid. If the total number of votes was 7500, the
number of valid votes that the other candidate got,
was:
(a) 2700
(b) 2900
(c) 3000
(d) 3100
(d) 11
4. In a two-digit, if it is known that its unit’s digit
exceeds its ten’s digit by 2 and that the product of
the given number and the sum of its digits is equal
to 144, then the number is:
8. A trader mixes 26 kg of rice at Rs. 20 per kg with
30 kg of rice of other variety at Rs. 36 per kg
and sells the mixture at Rs. 30 per kg. His profit
percent
(a) No profit, no loss
(a) 24
(b) 5%
(b) 26
(c) 8%
(c) 42
(d) 10%
(d) 46
5. Find a positive number which when increased by
17 is equal to 60 times the reciprocal of the number.
(a) 3
Department of Extension and Career Guidance
9. An industrial loom weaves 0.128 metres of cloth every second. Approximately, how many seconds will
it take for the loom to weave 25 metres of cloth?
(a) 178
(b) 195
80
Department of Extension and Career Guidance
(c) 204
(d) 488
10. A takes twice as much time as B or thrice as much
time as C to finish a piece of work. Working together, they can finish the work in 2 days. B can
do the work alone in:
(a) 4 days
(b) 6 days
(c) 8 days
(d) 12 days
11. The banker’s discount of a certain sum of money
is Rs. 72 and the true discount on the same sum
for the same time is Rs. 60. The sum due is:
(a) Rs. 360
(b) Rs. 432
(I) Total amount invested I the business in Rs.22,
000
(II) Profit earned at the end of 3 years is of the
total investment.
(III) The average amount of profit earned per year
is Rs.2750.
(a) (I) or (II) or (III)
(b) Either (III) only or (I) and (II) together
(c) Any two of the three
(d) All are required.
16. Twenty-four men can complete a work in sixteen
days. Thirty-two women can complete the same
work in twenty-four days. Sixteen men and sixteen women started working and worked for twelve
days. How many more men are to be added to
complete the remaining work in 2 days?
(c) Rs. 540
(a) 16
(d) Rs. 1080
(b) 24
(c) 36
12. In a regular week, there are 5 working days and for
each day, the working hours are 8. A man gets Rs.
2.40 per hour for regular work and Rs. 3.20 per
hours for overtime. If he earns Rs. 432 in 4 weeks,
then how many hours does he work for ?
(a) 160 hours
(b) 175 hours
(d) 48
17. A and B walk around a circular track. They start
at 8 a.m. from the same point in the opposite directions. A and B walk at a speed of 2 rounds
per hour and 3 rounds per hour respectively. How
many times shall they cross each other before 9.30
a.m.?
(c) 180 hours
(a) 5
(d) 195 hours
(b) 6
13. The ratio between the length and the breadth of a
rectangular park is 3 : 2. If a man cycling along
the boundary of the park at the speed of 12 km/hr
completes one round in 8 minutes, then the area of
the park (in sq. m) is:
(a) 15360
(b) 153600
(c) 30720
(d) 307200
(c) 7
(d) 8
18. A boat takes a total time of three hours to travel
downstream from P to Q and upstream back from
Q to P. What is the speed of the boat in still water?
(I) The speed of the river current is 1 km/hr.
(II) The distance between P and Q is 4 km.
(a) Only (I) is sufficient
(b) Only (II) is sufficient
14. A number when divided by 114 leaves the remainder 21. If the same number is divided by 19, then
the remainder will be:
(c) Both (I) and (II) are necessary to answer the
question.
(d) Either (I) or (II) alone is sufficient.
(a) 1
(b) 2
19. What percentage of simple interest per annum did
Anand pay to Deepak?
(c) 7
(d) 21
15. Three friends, P, Q and R started a partnership
business investing money in the ratio of 5 : 4 :
2 respectively for a period of 3 years. What is
the amount received by P as his share in the total
profit?
Department of Extension and Career Guidance
(I) Anand borrowed Rs.8000 from Deepak for
four years.
(II) Anand returned Rs.8800 to Deepak at the end
of two years and settled the loan.
(a) Only (I) is sufficient
(b) Only (II) is sufficient
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Department of Extension and Career
CHAPTER
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25. WEBSITE MODEL QUESTION PAPERS COLLECTION
(c) Both (I) and (II) are alone sufficient.
(a) 20
(d) (I) and (II) are not together sufficient.
(b) 10
20. If the radius of a circle is increased by 6%, then
the area is increased by:
(c) 15
(d) 18
23. How old was mother when Mohan was five years
old?
(a) 6%
(b) 12%
(a) 20
(c) 12.36%
(b) 30
(d) 16.64%
(c) 38
21. A wheel that has 6 cogs is meshed with a larger
wheel of 14 cogs. When the smaller wheel has
made 21 revolutions, then the number of revolutions made by the larger wheel is:
(d) 24
24. How old will Mohan be when his mother is 50?
(a) 20
(a) 4
(b) 15
(b) 9
(c) 25
(c) 12
(d) 35
(d) 49
25. How old was Mohans mother when he was born?
(Directions for questions 22 – 25): Mohan is
twice old al he was few years ago. His mother was
then six times as old as he was. She is now 35 years
old.
(a) 30
(b) 35
(c) 45
(d) 25
22. How old is Mohan?
Model Question Paper - 5
1. The average marks obtained by 22 candidates in
an examination is 45. The average of the first ten
is 55 while that of the last eleven is 40. The marks
obtained by the 11 candidates are
(a) 0
(b) 3
(c) 4
(d) None of these
2. he population of a town is 50,000. If the males
increase by 5% and females by 10% the population will be 53,500. Find the number of males and
females
(a) Male: 30,000 Female: 25,000
(b) Male: 25,000 Female: 25,000
(c) Male: 30,000 Female: 20,000
(d) Male: 20,000 Female: 30,000
3. A shopkeeper marks his goods 20% higher than the
cost price and allows discount of 5%. The percentage of his profit is
(a) 10%
(b) 14%
(c) 15%
Department of Extension and Career Guidance
(d) 13%
4. Of the three numbers, the first is twice the second,
and it is also thrice the third. If the average of the
three numbers is 44. Find the middle number
(a)
(b)
(c)
(d)
36
72
24
40
5. Ruchis house is to the right of Vanis house at a distance of 20 meters in the same row facing north.
Shabinas house is in the north east direction of
Vanis house at a distance of 25 meters. Determine
Ruchis house is in which direction with respect to
Shabinas house.
(a)
(b)
(c)
(d)
East
South
North-east
West
6. A can do a piece of work in 4 days and B can do
it in 12 days. What time will they require to do if
working together?
(a) 2 days
(b) 3 days
82
Department of Extension and Career Guidance
(c) 4 days
(d) 6 days
7. Rana travel 10 Km to the north, turns left and
travels 4 km, and then again turns right and covers another 5 km, and then turns right, and travels
another 4 km. How far is he from the right starting
point?
(a) 15 km
(b) 4 km
(c) 5 km
(d) 10 km
8. If a man covers 10.2 km in 3 hours, the distance
covered by him in 5 hours is
(a) 18 km
(b) 15 km
(c) 16 km
(d) 17 km
9. The value of 10 + 25 + 108 + 154 + 225 is
(a) 4
(b) 6
(c) 8
(d) 10
10. A sum of Rs. 12,500 amounts to Rs.15,500 in 4
years at the rate of Simple Interest. What is the
rate of interest?
(a) 3%
(b) 4%
(c) 5%
(d) 6%
11. The average temperature for Monday, Tuesday and
Wednesday was 38◦ and that for Tuesday, Wednesday and Thursday 40◦ . If the temperature on Monday was 39◦ , find the temperature on Thursday.
(a) 42◦
(b) 43◦
(c) 45◦
(d) 44◦
12. In a college election a candidate secured 62% of
the votes and is created by a majority of 144 votes.
The total number of votes poled is
(a) 500
(b) 600
(c) 300
(d) 400
Department of Extension and Career Guidance
13. In an examination 70% of the candidates passed
in English, 65% in Mathematics 27%failed in both
subjects, what is the pass percentage?
(a)
(b)
(c)
(d)
60%
62%
50%
55%
14. A man sells two houses at the rate of Rs.1.995 lakh
each. On one he gains 5% anad on the other he
loses 5%. His gain or loss percent in the whole
transaction is
(a)
(b)
(c)
(d)
0.25% loss
0.30% gain
0.1% loss
None of these
15. A car completes a certain journey in 8 hours. It
covers half the distance at 40km/hr and the rest
at 60km/hr. The length of the journey is
(a)
(b)
(c)
(d)
350
420
384
400
km
km
km
km
16. 50 × 98 is equal to
(a)
(b)
(c)
(d)
63.75
65.95
70
70.25
17. A sum of money at Simple Interest amounts to Rs.
815 in 3 years and to Rs. 854 in 4 years. The sum
is
(a)
(b)
(c)
(d)
Rs.
Rs.
Rs.
Rs.
650
690
698
700
18. Mani and Ravi can complete a work in 5 and 20
days respectively. Ravi starts the work and after
five days Mani also joins him. In all, in how many
days the work would be completed.
(a) 3 days
1
(b) 4 days
4
(c) 5 days
(d) None of these
19. By selling an umbrella for Rs. 300, shopkeeper
gains 20%, during a clearance sale, the shopkeeper
allows a discount of 10% on the marked price. His
gain percent during the sale is:
(a) 7%
(b) 7.5%
83
Department of Extension and Career
CHAPTER
Guidance
25. WEBSITE MODEL QUESTION PAPERS COLLECTION
(c) 8%
23. Division : Section ::
(d) 9%
(a) Layer : Tier
20. A, B and C can do a piece of work in 8, 16 and 24
days respectively. They together will complete the
work in
(b) Tether : Bundle
(c) Chapter : Verse
(d) Dais : Speaker
(a) 5 days
24. Here are some words translated from an artificial
language.
(b) 6 days
4
(c) 4
days
11
1
(d) 7 days
3
hapllesh means cloudburst
srenchoch means pinball
resbosrench means ninepin
21. Look carefully for the pattern, and then choose
which pair of numbers comes next. 42 40 38 35 33
31 28
Which word could mean ”cloud nine”?
(a) leshsrench
(a) 25 22
(b) ochhapl
(b) 26 23
(c) haploch
(c) 26 24
(d) hapleresbo
(d) 26 22
25. Find the missing number in the series? 6, 12, 21,
?, 48
22. Diploma is related with
(a) Principal
(a) 38
(b) Curriculam
(b) 40
(c) Employment
(c) 45
(d) Graduation
(d) 33
Model Question Paper - 6
1. A housewife saved Rs. 2.50 in buying an item
on sale. If she spent Rs. 25 for the item, approximately how much per cent she saved in the
transaction?
(a) 8%
(b) 9%
(c) 10%
(d) 11%
Answer: (b)
C.P. = Rs. (25 + 2.50) =Rs. 27.50
Profit = Rs. 2.50
2.5
Profit
× 100 =
× 100 = 9.1%
Profit% =
C.P.
25
2. If 120 is 20% of a number, then 120% of that number will be:
(a) 20
(b) 120
(c) 360
(d) 720
Department of Extension and Career Guidance
Answer: (d)
Let the number be x.
Given: 120 = 20% × x
120 × 100
⇒x=
= 600
20
120
∴ 120% × x =
× 600 = 720.
100
3. A sum of Rs. 1360 has been divided among A, B
and C such that A gets 2/3 what B gets, and B
gets 1/4 of what C gets. Bs share is
(a) Rs. 120
(b) Rs. 160
(c) Rs. 240
(d) Rs. 300
Answer: (c)
2
Given: A = × B.
3
1
B = × C ⇒ C = 4B.
4
∴ B’s share
84
Department of Extension and Career Guidance
(a) 3
=
=
=
=
=
B
× 1360
A+B+C
B
× 1360
2
× B + B + 4B
3
B
× 1360
2
B
+1+4
3
1
× 1360
17
3
3
1360 = 240
17
(b) 14
(c) 16
(d) 17
Answer: (a)
Given:
128/16×? − 7 × 2
72 − 8 × 6+?2
128/16×? − 7 × 2
=
1
=
72 − 8 × 6+?2
8×? − 14
=
49 − 48+?2
0
=
?2 − 8×? + 15
0
=
(? − 3)(? − 5)
√
4.
625
14
11
×√ ×√
is equal to
11
25
196
(a) 5
(b) 6
∴ ? = 3, 5.
√
8. If 18 × 14×? = 84, then ? equals:
(c) 8
(a) 22
(d) 11
(b) 24
(c) 28
Answer: (a)
(d) 32
√
625
14
11
×√ ×√
11
25
196
=
25 14 11
×
×
=5
11
5
14
Answer: (c)
√
5.
√
0.0025 ×
√
2.25 × 0.0001 =?
18 × 14×?
=
84
18 × 14×?
=
84 × 84
(a) 0.000075
(b) 0.0075
9. The average temperature of the town in the first
four days of a month was 58 degrees. The average
(d) None of these
for the second, third, fourth and fifth days was 60
degrees. The temperature of the first and fifth days
Answer: (d)
were in the ratio 7:8, then what is the temperature
on the fifth day?
√
√
0.0025 × 2.25 × 0.0001 = 0.05 × 1.5 × 0.01 = .00075
(a) 64
(c) 0.075
6. An employer pays Rs.20 for each day a worker
works, and forfeits Rs.3 for each day he is idle.
At the end of 60 days, a worker gets Rs.280 for
how many days did the worker remain idle?
(a) 30
(b) 50
(c) 40
(d) 20
Answer: (c)
7. Which of the following will come in place of both
the question marks in the following equation?
128/16×? − 7 × 2
=1
72 − 8 × 6+?2
Department of Extension and Career Guidance
(b) 62
(c) 66
(d) None of these
Answer: (a)
Given:
I + II + III + IV
= 58
4
⇒ I + II + III + IV = 58 × 4 = 232
II + III + IV + V
= 60
4
⇒ II + III + IV + V = 60 × 4 = 240 I : V =
I
7
7:8⇒
= ⇒ 8I − 7V = 0. From first data,
V
8
I − V = −8.
Solving last two equations for V, we get V = 64
10. Successive discounts of 10%, 12% and 15%
amounts to a single discount of:
85
Department of Extension and Career
CHAPTER
Guidance
25. WEBSITE MODEL QUESTION PAPERS COLLECTION
(a) 32.68%
13. A shopkeeper earns a profit of 12% on selling a
book at 10% discount on the printed price. The
ratio of the cost price to the printed price of the
book is
(b) 35.28%
(c) 36.68%
(d) None of these
(a) 45:56
Answer: (d)
(b) 50:61
10 + 12
= 22 + 0.22 = 22.22
100
22.22 + 15
• 22.22 + 15 +
= 37.22 + 0.3722 =
100
37.5922
• 10 + 12 +
11. A and B can do a work is 8 days B and C can do
the same work in 12 day. A, B and C together can
finish it in 6 days, A and C together will do it in:
(c) 55:69
(d) 99:125
14. A man can do a piece of work in 5 days, but with
the help of his son, he can do it in 3 days, In what
time can his son do it alone?
(a) 6.5 days
(b) 7 days
(a) 4
(c) 7.5 days
(b) 6
(d) 8 days
(c) 8
15. A man on tour travels first 160 km at 64 km/hr
and the next 160 km at 80 km/hr. The average
speed for the first 320 km of the tour is :
(d) 12
Answer: (c)
(a) 35.55 kmph
1
.
8
1
(2) B and C 1 day’s work =
.
12
1
(3) A, B and C 1 day’s work = .
6
(5) Adding (1) and (2), we get A, 2B and C 1
1
5
1
=
.
day’s work = +
8 12
24
1
(6) From (3), 2A, 2B and 2C 1 day’s work = .
3
(7) Subtracting (6) from (5), we get, B 1 day’s
1
work = .
8
(1) A and B 1 day’s work =
12. A grocer has a sale of Rs. 6435, Rs.6927, Rs.6855,
Rs.7230 and Rs.6562 for 5 consecutive months.
How much sale he have in the sixth month so that
he gets an average sale of Rs. 6500?
(b) 36 kmph
(c) 71.11 kmph
(d) 71 kmph
16. Two trains 140 m and 160 m long run at the speed
of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time (in sec)
which they take cross each other is:
(a) 9
(b) 9.6
(c) 10
(d) 10.8
17. Two equal sums of money were lent at simple in1
1
terest at 11% per annum for 3 years and 4 years
2
2
respectively. If the difference in interests for two
periods was Rs. 412.50 then each sum is
(a) Rs. 4991
(a) Rs. 3250
(b) Rs. 5991
(b) Rs. 3500
(c) Rs. 6001
(c) Rs. 3750
(d) Rs. 6991
(d) Rs. 4250
Answer: (a)
Average
34009 + x
6
34009 + x
x
18. Two third of three fifth of one fourth of a number
is 24. What is 30% of that number?
=
Sum of observations
No. of observations
=
6500
(b) 72
=
6500 × 6 = 39000
(c) 90
=
39000 − 34009 = 4991.
(d) 69
Department of Extension and Career Guidance
(a) 42
86
Department of Extension and Career Guidance
Answer: (b)
Given:
2 3 1
× × × x = 24.
3 5 4
3 5 4
x = 24 × × × = 240
2 3 1
30
Requires Answer =
× 240 = 72.
100
(c) PRVX
(d) MQTV
22. Except one, all are in a certain way, select the alternative which is different from others.
(a) A
(b) U
19. The value of
1
(c) Y
1
2+
2+
(d) O
1
1
2−
2
23. Pole is related to magnet in the same way as
is related to Battery.
8
19
3
(b)
8
19
(c)
8
8
(d)
3
(a)
(a) Cell
(b) Power
(c) Terminal
(d) Energy
20. A farmer took a loan at 12% per annum at simple
interest. After four years he settled the loan by
paying Rs. 2442 what was the principal amount?
24. Which of the following figures represents Furniture,
Chairs and Tables?
(a) A
(b) B
(a) Rs. 1542
(c) C
(b) Rs. 1600
(d) D
(c) Rs. 1650
25. 8: 81::64:?
(d) Rs. 1550
21. Except one, all are in a certain way, select the alternative which is different from others.
(a) 525
(b) 125
(a) BFIK
(c) 137
(b) DHKM
(d) 625
Model Question Paper - 7
1. The average marks obtained by 22 candidates in
an examination is 45.The average of first ten is 55
while that of the last eleven is 40.The marks obtained by the eleventh candidate is
(a) 0
(b) 3
(c) 4
(d) None of these
2. he population of a town is 50,000. If the males
increase by 5% and females by 10% the population will be 53,500. Find the number of males and
females
(a) Male: 30,000 Female: 25,000
(b) Male: 25,000 Female: 25,000
(c) Male: 30,000 Female: 20,000
(d) Male: 20,000 Female: 30,000
Department of Extension and Career Guidance
3. The average weight of 8 persons is increased by
3.5kg. When one of them, whose weight is 56kg,
is replaced by a new man, the weight of the new
man is.
(a)
(b)
(c)
(d)
64 kg
84 kg
80 kg
None of these
4. In a class of twenty students the average is
13years.By the inclusion of the teachers age the
average age is increased by 2 years. What is the
age of the teacher.
(a)
(b)
(c)
(d)
60 years
54 years
55 years
None of these
87
Department of Extension and Career
CHAPTER
Guidance
25. WEBSITE MODEL QUESTION PAPERS COLLECTION
5. x, y and z can do a piece of work in 4, 6 and 8
days respectively. They together will complete the
work in.
(a) 5 days
11
days
(b) 1
13
(c) 6 days
4
(d) 4
days
11
6. Of the three numbers, the first is twice the second,
and it is also twice the third. If the average of three
numbers is 40. Find the middle number.
(a) 4287
(b) 4827
(c) 4278
(d) 8724
12. Find the value of x.
8
1
1
4
1
6
7
3
2
8
3
x
(a) 0
(b) 5
(c) 4
(a) 72
(d) 2
(b) 24
(c) 34
(d) 30
7. If the three fifth of a number is 50 more than 50%
of the same number. What is the number.
(a) 50
(b) 100
13. 6482 is 4826, 3901 is 9013 and 5893 is?
(a) 8935
(b) 8953
(c) 8539
(d) 8359
14. 4 × 8 = 2, 5 × 10 = 2, 6x24 = 4, ×7x35 =?
(c) 500
(a) 3
(d) 555
(b) 4
8. In an examination 30% of total student failed in
English, 40% failed in Hindi and 15% in both. The
percentage of those who passed in both subject is.
(a) 40%
(c) 5
(d) 10
15. Think of a number, divide it by 2 and add 4 to it,
result is 36, find the number.
(b) 30%
(a) 18
(c) 20%
(b) 24
(d) None of these
(c) 44
9. The ratio between the present ages of P and Q is
6:7.If Q is 4years old than P, what will be the ratio
of ages of P and Q after 4 years.
(d) 64
16. Find out of the next two letters of the given series:
A,Z,D,X,G,V,J,T,M,?,?
(a) 3:4
(b) 7:8
(c) 4:3
(d) 3:5
10. Seetha travel 10km to the north, turns left and
travels 4km and then again turns right and covers
another 5km, and then turns right, and travels another 4km. How far is she from the right starting
point?
(a) R, P
(b) S, N
(c) P, R
(d) N,S
17. Find the missing number in the series.
6, 12, 21, ?, 48
(a) 27
(a) 15 km
(b) 30
(b) 4 km
(c) 33
(c) 5 km
(d) 10 km
11. MORE=7248, ROME=?
Department of Extension and Career Guidance
(d) 36
18. Find the missing numbers?
64, 32, 35, 5, 22, 11, 14, ?
88
Department of Extension and Career Guidance
(a) 2
(c) 387
(b) 4
(d) None of these
(c) 6
20. In the series BAC, EDF, HGI, the blank space
refers to
(d) 8
19. Complete the series:
If AD is 31, BC is 27, EG is 48 then what is ACG?
(a) JKL
(b) LKJ
(a) 324
(c) IJK
(b) 378
(d) KJL
Arithmetic - Model Question Paper - I
1. A man buys a cycle for Rs. 1400 and sells it at a
loss of 15%. What is the selling price for the cycle?
(a) Rs. 1202
(b) Rs. 1190
(c) Rs. 1160
(d) Rs. 1000
2. The ratio of cost price and selling price is 5:4. The
loss percentage is
(a) 20%
(b) 25%
(c) 40%
(d) 50%
3. A shopkeeper sells two TV sets at the same price.
There is a gain of 20% on one TV and a loss of 20%
on the other. Which of the following statement is
correct?
(a) The shopkeeper makes no net gain or profit.
(b) The shopkeeper losses by 2%
(c) The shopkeeper gains by 2%
(d) The shopkeeper losses by 4%
4. If the cost price of 15 tables be equal to the selling
price of 20 tables, the loss per cent is
(a) 20%
(b) 30%
(c) 25%
(d) 37.5%
5. A cistern can be filled with water by a pipe in 5
hours and it can be emptied by a second pipe in
4 hours. If both the pipes are opened when the
cistern is full, the time in which it will be emptied
is
(a) 9 hours
(b) 18 hours
Department of Extension and Career Guidance
(c) 20 hours
1
(d) 20 hours
2
6. A and B can do a piece of work in 10 days, B and
C in 15 days and C and A in 20 days. C alone can
do the work in
(a)
(b)
(c)
(d)
60 days
120 days
80 days
30 days
2
7. A can cultivate th of a land in 6 days and B can
5
1
cultivate rd of the same land in 10 days. Working
3
4
together A and B can cultivate th of the land in
5
(a) 4 days
(b) 5 days
(c) 8 days
(d) 10 days
8. A does half as much work as B in one sixth of the
time. If together they take 10 days to complete a
work, how many time shall B take to do it alone?
(a)
(b)
(c)
(d)
70
30
40
50
days
days
days
days
9. The value of
(a)
(b)
(c)
(d)
√
0.000441 is equal to
0.21
0.0021
0.021
0.00021
10. The value of 0.008 × 0.01 × 0.072 ÷ (0.12 × 0.0004)
is
(a) 1.2
(b) 0.12
(c) 0.012
89
Department of Extension and Career
CHAPTER
Guidance
25. WEBSITE MODEL QUESTION PAPERS COLLECTION
16. The value of
(d) 1.02
1
11. Simplify
3+
(6.25)1/2 × (0.0144)1/2 + 1
.
(0.027)1/3 × (81)1/4
(a) 0.14
(c) 1
(d) 1.4
1
3
1
of of a number is 2 of 10. What is the num2
4
2
ber?
(a) 50
(b) 60
1
7
9
12
22
22
(b)
5
5
(c)
22
(d) 1
17. The difference between the simple and compound
interest on a certain sum of money for 2 years at
4% per annum is Re. 1. The sum is
(a)
(b)
(c)
(d)
2
(c) 66
3
(d) 56
13. The value of
2
3
×
1
5 2
3
÷ of 1
6 3
4
(a) 2
(b) 1
(c) 1/2
(d) 2/3
14. Which of the following fractions is smallest?
8 14 7 11
, , , .
15 33 13 13
8
15
7
(b)
13
11
(c)
13
14
(d)
33
(a)
15. Find the sum of the following:
1 1
1
1
1
1
1
1
+ +
+
+
+
+
+ .
9 6 12 20 30 42 56 72
1
(a)
2
(b) 0
1
(c)
9
(d)
2−
77
.
22
(a)
(b) 1.4
12.
+
1
1
2520
Department of Extension and Career Guidance
Rs. 250
Rs. 240
Rs. 260
None of these
18. A sum of money doubles itself in 4 years at compound interest. It will amount to 8 times itself at
the same rate of interest in
(a)
(b)
(c)
(d)
18
12
16
24
years
years
years
years
19. A sum of money invested at compound interest
amounts to Rs. 650 at the end of first year and
Rs. 676 at the end of second year. The sum of
money is
(a)
(b)
(c)
(d)
Rs.
Rs.
Rs.
Rs.
600
540
625
560
20. A sum of Rs. 1550 was lent partly at 5% and partly
at 8% simple interest. The total interest received
after 3 years is Rs. 300. The ratio of money lent
at 5% to that at 8% is
(a)
(b)
(c)
(d)
5:8
8:5
31:6
16:15
2
21. In what time will the simple interest be
of the
5
principal at 8 per cent per annum?
(a)
(b)
(c)
(d)
8
7
5
6
years
years
years
years
90
Department of Extension and Career Guidance
22. The perimeter of two squares are 24 cm and 32 cm.
The perimeter (in cm) of a third square equal in
area to the osum of the areas of these squares is
(a) 45
(b) 40
(c) 32
(d) 48
23. The length of a rectangular garden is 12 m and its
breadth is 5 m. Find the length of the diagonal of
a square garden having the same area as that of
the rectangular garden
√
(a) 2 30 m
√
(b) 13 m
(c) 13 m
√
(d) 8 15 m
24. The base of a triangle is 15 cm and height is 12
cm. The height of another triangle of double the
area having the base 20 cm is
1
2
1
(b) 4
6
1
(c) 9
2
2
(d)
9
(a) 4
29. The value of
s √
(a)
(b)
√
√
√
6−
6+
√
√ √
√ 8
3− 2
√
.
5 + 24
2
2
6−2
√
(d) 2 − 6
√
30. If 4096 = 64, then the value of
√
√
√
40.96 0.004096 + 0.00004096
(c)
upto two places of decimals is
(a) 9 cm
(a) 7.09
(b) 18 cm
(b) 7.10
(c) 8 cm
(c) 7.11
(d) 12.5 cm
(d) 7.12
25. The diagonals of a rhombus are 32 cm and 24 cm
respectively. The perimeters of the rhombus is
√
12 −
31. 8.31+0.6+0.002 is equal to
(a) 8.912
(a) 80 cm
(b) 8.921
(b) 72 cm
(c) 8.979
(c) 68 cm
(d) 64 cm
26. What is the volume √
of a cube (in cubic cm) whose
diagonal measures 4 3 cm?
(a) 16
(b) 27
(c) 64
(d) 8
27. A wire when bent in the form of a square encloses
an area of 484 sq. cm. What will be the enclosed
area when the same wire is bent into the form of a
circle?
(d) 8.997
1/2
32. Simplify: 642/3 × 2−2 ÷ 80
.
(a) 0
(b) 1
(c) 2
(d) 1/2
s
33. The value of
(0.1)2 + (0.01)2 + (0.009)2
.
(0.01)2 + (0.001)2 + (0.0009)2
(a) 100
(b) 10
(c) 0.1
(a) 462 sq. cm
(b) 539 sq. cm
(c) 616 sq. cm
(d) 693 sq. cm
28. Simplify:
1 1
1 1
1 1 1
1 − −
.
8 3 ÷ 1 −
2 4
4 2
2 3 6
Department of Extension and Career Guidance
(d) 0.01
34. Find the value of (0.98)3 + (0.02)3 + 3 × 0.98 ×
0, 02 − 1.
(a) 1.98
(b) 1.09
(c) 1
(d) 0
91
Department of Extension and Career
CHAPTER
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25. WEBSITE MODEL QUESTION PAPERS COLLECTION
35. If a ∗ b = 2(a + b), then 5 ∗ 2 is equal to
Year
Men
Women
Children
Total
1988
1989
1990
1991
1992
65104
70391
69395
71274
60387
62516
63143
65935
20314
21560
23789
146947
153922
160998
(a) 3
(b) 10
(c) 14
(d) 20
3
3
3
3
36. If 1 + 2 + 3 + · · · + 10 = 3025, then find the
value of 23 + 43 + 53 + · · · + 203 .
(a) 6050
(b) 9075
Increase (+)
or decrease
(-) over
preceding
year
+(11630)
-(5337)
-
42. The number of children in 1988 is
(c) 12100
(a) 31236
(d) 24200
(b) 125491
37. Which of the following numbers is the least?
(a) 0.52
√
(b) 0.49
√
(c) 3 0.008
(d) 0.23
38. 0.15% of 33
(c) 14546
(d) 21456
43. The total population in 1989 is
(a) 144537
(b) 158577
1
of Rs. 10000 is
3
(a) Rs. 5
(c) 146947
(d) 149637
44. Number of children in 1989 is
(b) Rs. 150
(a) 25670
(c) Rs. 0.05
(b) 14040
(d) Rs. 105
39. 30% of x is 72. The value of x is
(a) 216
(c) 13970
(d) 15702
45. Number of women in 1991 is
(b) 240
(a) 57630
(c) 480
(b) 56740
(d) 640
(c) 52297
(d) 62957
40. If 15% of (A + B) = 25% of (A − B), then what
percentage of B is equal to A?
(a) 10%
46. Increase or decrease of population in 1992 over
1991 is
(a) -(12413)
(b) 60%
(b) +(12413)
(c) 200%
(c) +155661
(d) 400%
(d) +7086
41. If a number x is 10% less than another number y
and y is 10% more than 125, then x is equal to
(a) 150
(b) 143
(c) 140.55
(d) 123.75
Following table gives the population of a locality from 1988 to 1992. Read the table
and answer the questions 42 to 46.
Department of Extension and Career Guidance
47. The average age of 30 boys in a class is 15 years.
One boy aged 20 years, left the class, but two new
boys came in his place whose ages differ by 5 years.
If the average age of all the boys now in the class
becomes 15 years, the age of the younger newcomer
is
(a) 20 years
(b) 15 years
(c) 10 years
(d) 8 years
92
Department of Extension and Career Guidance
48. Out of three numbers, the first is twice the second
and is half of the third. If the average of the three
numbers is 56, then the difference of first and third
numbers is
(a) 12
(b) 20
(c) 24
(d) 48
49. The average age of 8 persons is increased by 2
years, when one of them, whoseage is 24 years is
replaced by a new person. The age of the new
person is
(a) 42 years
(b) 40 years
(c) 38 years
(d) 45 years
50. If the volumes of the two cubes are in the ratio
27:64, then the ratio of their total surface areas is
(a) 27:64
(b) 3:4
(c) 9:16
(d) 3:8
51. The base radii of two cylinders are in the ratio 2:3
and their heights are in the ratio 5:3. The ratio of
their volumes is
(a) 27:20
(b) 20:27
(c) 9:4
(d) 4:9
52. The slant height of a conical mountain is 2.5 km
and the area of its base is 1.54 km2 . Taking
22
, the height of the mountain is
π=
7
(a) 2.2 km
(b) 2.4 km
(c) 3 km
(d) 3.11 km
53. A hemisphere and a cone have equal bases. If their
heights are also equal, the ratio of their curved surfaces will be
√
(a) 1 : 2
√
(b) 2 : 1
(c) 1:2
(d) 2:1
54. Three solid metallic spheres of diameters 6 cm, 8
cm and 10 cm are melted and recast into a new
solid sphere. The diameter of the new sphere is
Department of Extension and Career Guidance
(a) 4 cm
(b) 6 cm
(c) 8 cm
(d) 10 cm
55. If
2a + b
a+b
= 3 then find the value of
.
a + 4b
a + 2b
5
9
2
(b)
7
10
(c)
9
10
(d)
7
(a)
56. If a:b=2:3 and b:c=4:5, find a2 : b2 : bc.
(a) 4:9:45
(b) 16:36:45
(c) 16:36:20
(d) 4:36:20
1 3
1 5
5 3
57. If A : B = : , B : C = : , C : D = :
2 8
3 9
6 4
then the ratio A : B : C : D is
(a) 6:4:8:10
(b) 6:8:9:10
(c) 8:6:10:9
(d) 4:6:8:10
58. Two numbers are in the ratio 5:7. On diminishing
each of them by 40, they become in the ratio 17:27.
The difference of the numbers is
(a) 18
(b) 52
(c) 137
(d) 50
59. The ratio of the number of boys and girls of a
school with 504 students is 13:11. What will be
the new ratio if 12 more girls are admitted?
(a) 91:81
(b) 81:91
(c) 9:10
(d) 10:9
60. A and B have monthly incomes in the ratio 5:6
and monthly expenditures in the ratio 3:4. If they
save Rs. 1800 and Rs. 1600 respectively, find the
monthly income of B.
(a) Rs. 3400
(b) Rs. 2700
(c) Rs. 1720
93
Department of Extension and Career
CHAPTER
Guidance
25. WEBSITE MODEL QUESTION PAPERS COLLECTION
(d) Rs. 7200
q
p
√
61. The value of 2 + 2 + 2 + · · · is
(a) 2
√
(b) 2
√
(c) 2 2
√
(d) 2 + 2
62. Arrange
√
√ √the√ following in descending order:
3
4, 2, 6 3, 4 5.
√
√
√
√
(a) 3 4 > 4 5 > 2 > 6 3
√
√
√
√
(b) 4 5 > 3 4 > 6 3 > 2
√
√
√
√
(c) 2 > 6 3 > 3 4 > 4 5
√
√
√
√
(d) 6 3 > 4 5 > 3 4 > 2
63. Simplify:
(1.53)3 + (4.7)3 + (3.8)3 −
3 × 1.5 × 4.7 × 3.8
− 1.5 × 4.7 − 4.7 × 3.8 −
(1.5)2 + (4.7)2 + (3.8)2
3.8 × 1.5
67. Two numbers are respectively 20% and 50% of a
third number. What per cent is the first number
of the second?
(a) 10%
(b) 20%
(c) 30%
(d) 40%
68. Out of her total income, Neelam spends 20% on
house rent and 70% of the rest on household expenditure. If she saves Rs. 3600, what is her total
income?
(a) Rs. 15000
(b) Rs. 10500
(c) Rs. 10050
(d) Rs. 10000
69. Income of A is 10% more than income of B. Let
B’s income be x% less than A’s income. Find x.
(c) 10
1
%
11
1
(b) 10 %
11
(c) 11%
(d) 30
(d) 10%
(a) 9
(a) 0
(b) 1
14
64. The product of two fractions is
and their quo15
35
tient is
. The greater fraction is
24
7
4
7
(b)
6
7
(c)
3
4
(d)
5
(a)
65. The sum of the squares of two positive numbers is
100 and difference of their squares is 28. Fid the
sum of the numbers.
(a) 12
(b) 13
70. Salary of a person is first increased by 20% then
decreased by 20%. Change in his salary is
(a) 4% decreased
(b) 4% increased
(c) 8% decreased
(d) 20% increased
71. A fruit seller had some apples. He sells 40% apples
and still has 420 apples. Originally, he had
(a) 588 apples
(b) 600 apples
(c) 672 apples
(d) 700 apples
72. If the price of rice is reduced by 20%, one can buy
2 kg more for Rs. 100. The reduced price of rice is
(a) Rs. 50 per kg
(c) 14
(b) Rs. 10 per kg
(d) 15
(c) Rs. 40 per kg
66. The LCM of two numbers is 1820 and their HCF
is 26. If one number is 130 then the other number
is
(d) Rs. 5 per kg
73. If I would have purchased 11 articles at the rate of
10 for Rs. 11, the profit per cent would have been
(a) 70
(a) 10%
(b) 1690
(b) 11%
(c) 364
(c) 21%
(d) 1264
(d) 100%
Department of Extension and Career Guidance
94
Department of Extension and Career Guidance
74. By selling an article for Rs. 72, there is a loss of
10%. In order to gain 5%, its selling price should
be
(a) Rs. 87
(b) Rs. 85
(c) Rs. 80
(d) Rs. 84
75. An article is sold at a loss of 10%. Had it been
sold for Rs. 9 more, there would have been a gain
1
of 12 % on it. The cost price of the article is
2
(a) Rs. 40
(b) Rs. 45
(c) Rs. 50
(d) Rs. 35
76. A dealer offers a discount of 10% on the marked
price of an article and still makes a profit of 20%.
If its marked price is Rs. 800, then the cost price
of the article is
(a) Rs. 900
(b) Rs. 800
(a) 14 hours
(b) 7 hours
(c) 8 hours
(d) 16 hours
81. A train is 125 m long. If the train takes 30 seconds
to cross a tree by the railway line, then the speed
of the train is
(a) 14 kmph
(b) 15 kmph
(c) 16 kmph
(d) 12 kmph
82. A train passes two bridges of lengths 800 m and
400 m in 100 seconds and 60 seconds respectively.
The length of the train is
(a) 80 m
(b) 90 m
(c) 200 m
(d) 150 m
83. The ratio of two numbers is 3:4 and their HCF is
4. Their LCM is
(c) Rs. 700
(a) 12
(d) Rs. 600
(b) 16
77. Successive discounts of 20% and 10% are equivalent to a single discount of
(a) 30%
(b) 15%
(c) 28%
(d) 25%
78. The marked price of a watch is Rs. 1000. A retailer
buys it at Rs. 810 after getting two successive discounts of 10% and another rate which is illegible.
What is the second discount rate?
(a) 15%
(c) 24
(d) 48
84. The divisor is 25 times the quotient and 5 times
the remainder. If the quotient is 16, the dividend
is
(a) 6400
(b) 6480
(c) 400
(d) 480
85. Find the least multiple of 23, which when divided
by 18, 21 and 24 leaves remainder 7, 10 and 13
respectively
(b) 10%
(c) 8%
(d) 6.5%
(a) 3013
(b) 3024
(c) 3002
79. An athlete runs 200 m race in 24 seconds. His
speed (in kmph) is
(a) 20
(d) 3036
86. If
50
=
∗
(b) 24
(c) 28.5
(d) 30
7
80. A train runningat
of its own speed reached a
11
place in 22 hours. How much time could be saved
if the train would run as its own speed?
Department of Extension and Career Guidance
∗
, then the value of ∗ is
1
12
2
25
2
4
(b)
25
(c) 4
(a)
(d) 25
95
Department of Extension and Career
CHAPTER
Guidance
25. WEBSITE MODEL QUESTION PAPERS COLLECTION
87. Three fifth of the square of a certain number is
126.15. What is the number?
(a) Rs. 600
(b) Rs. 1000
(a) 210.25
(c) Rs. 900
(b) 75.69
(d) Rs. 1200
(c) 14.5
(d) 145
88. Find the greatest number of five digits which when
divided by 3, 5, 8 and 12 have 2 as remainder.
(a) 99999
(b) 99958
(c) 99960
(d) 99962
4
89. What fraction of must be added to itself to make
7
1
the sum
.
14
7
8
1
(b)
2
4
(c)
7
15
(d)
14
(a)
90. The smallest number added to 680621 to make the
sum a perfect square is
(a) 4
(b) 5
(c) 6
(d) 8
91. If 5 men or 8 women can do a piece of work in 12
days, how many days will be taken by 2 men and
4 women to do the same work?
(a) 15 days
(b) 13.5 days
1
(c) 13 days
3
(d) 10 days
92. Harsha is 40 years old and Rith is 60 years old.
How many years ago was the ratio of their ages
3:5?
(a) 10 years
(b) 20 years
(c) 37 years
(d) 5 years
93. A sum of Rs. 9000 is to be distributed among A,
B and C in the ratio 4:5:6. What will be the difference between A’s and C’s shares?
Department of Extension and Career Guidance
94. Zinc and Copper are in the ratio of 5:3 in 200 grams
of an alloy. How much grams of copper be added
to make the ratio as 3:5?
1
(a) 133
3
1
(b)
200
(c) 72
(d) 66
95. The price of 1o chairs is equal to that of 4 tables.
The price of 15 chairs and 2 tables together is Rs.
4000. The total price of 12 chairs and 3 tables is
(a) Rs. 3750
(b) Rs. 3840
(c) Rs. 3500
(d) Rs. 3900
96. The sum of three consecutive odd natural numbers
is 87. The smallest of these numbers is
(a) 29
(b) 31
(c) 23
(d) 27
4
of an estate be worth Rs. 16800, then the
5
3
value of of it is
7
97. If
(a) Rs. 90000
(b) Rs. 9000
(c) Rs. 72000
(d) Rs. 21000
98. Two numbers are in the ratio 2:3. If 3 be added to
both of them, then their ratio becomes 3:4. Find
the sum of the numbers
(a) 10
(b) 15
(c) 90
(d) 25
99. 4 bells ring at intervals of 30 minutes, 1.5 hours, 1
hour, 1 hour and 45 minutes respectively. All the
bells ring simultaneously at 12 noon. They will
again ring simultaneously at
(a) 12 mid-night
(b) 3 a.m.
(c) 6 a.m.
96
Department of Extension and Career Guidance
(d) 9 a.m.
6
100. A boy on being asked what
of certain fraction
7
was, made the mistake of dividing the fraction by
6
and so got an answer which exceeded the correct
7
13
answer by
. Find the fraction.
70
Department of Extension and Career Guidance
2
3
3
(b)
5
4
(c)
5
7
(d)
9
(a)
97
Department of Extension and Career
CHAPTER
Guidance
25. WEBSITE MODEL QUESTION PAPERS COLLECTION
Arithmetic - Model Question Paper II
1
3
1
(c)
9
3
(d)
7
1. 53753+3299+1387=
(b)
(a) 58349
(b) 58439
(c) 58429
(d) 58339
9. Evaluate:
2. What is 60% of 120?
69842 × 69842 − 30158 × 30158
69842 − 30158
(a) 56
(b) 64
(a) 30158
(c) 72
(b) 39684
(d) 80
(c) 69842
(d) 1000000
3. Simplify: 100.75 ÷ 25
10. In order to produce a multiple of 852, what is the
least number which should be multiple with 715?
(a) 4.3
(b) 4.03
(a) 10
(c) 4.003
(b) 12
(d) 0.403
(c) 15
2
4. What is the value of (0.03) ?
11. A number is 25 more than its 2/5. What is the
number?
(a)
(b)
(c)
25
7
125
(b)
3
(c) 60
(a)
(d)
5. What is the value of
(d) 35
272 − 252
?
27 − 25
(d) 80
(a) 52
12. Which is the smallest number that will give a perfect square, when subtracted from the sum of the
squares of 11 and 13?
(b) 50
(c) 92
(d) 108
(a) 1
6. Which one of the following is a perfect square?
(b) 11
(a) 5489649
(c) 5
(b) 847842
(d) 9
13. 11 times a number gives 176. What is the number?
(c) 487893
(d) 442007
(a) 1936
(b) 165
7. Simplify: (4.5 × 18)2 .
(c) 263
(a) 6461
(d) 16
(b) 6561
14. The sum of the numbers is 100 and their difference
is 37. What is the difference of their squares?
(c) 6571
(d) 6581
3 2
1 7
+
−
8. + −
7
9
9 9
2 =?
9
1
(a)
7
Department of Extension and Career Guidance
(a) 6300
(b) 3700
(c) 1000
(d) 100
98
Department of Extension and Career Guidance
15. The number zero flanked by the same two digit
number on left and right sides; for example, 32032
and 63063. Which largest number will always divide such a number?
(a) 7
(b) 13
(c) 89
(d) 1001
16. Which is the least square number exactly divisible
by 20, 15, 12 and 5.
(a) 14400
(b) 3600
(c) 1200
(d) 900
17. 10002 − 9992 =?
(a) 1999
(b) 1000
(c) 999
(d) 1
18. A number when divided by 27 leaves a remainder
of 13. What would be the remainder if the number
is divided by 9?
(a) 4
(b) 5
(c) 6
(d) 7
19. If a number gives a remainder 83 when divided by
123. What remainder shall it give when divided by
41?
(a) 0
(b) 1
(c) 40
22. Rs. 800 will fetch a compound interest of Rs. 82
at 5% per year in how many years?
(a)
(b)
(c)
(d)
4
2
3
5
years
years
years
years
23. A man purchases a calculator which has a printed
price of Rs. 160. He gets two successive discounts
of 20% and 10%. How much did he pay?
(a)
(b)
(c)
(d)
Rs.
Rs.
Rs.
Rs.
129.60
119.60
115.70
112
24. A shopkeeper enhances his cost price of a product
by 20% and allows a discount of 10%. What is his
net profit?
(a)
(b)
(c)
(d)
15%
12%
10%
8%
25. The average runs of first five batsman is 46 and
that of the first four is 45. What is the score of
fifth batsman?
(a)
(b)
(c)
(d)
15
10
25
50
26. One tap fills a tank in 8 hours and another empties
it in 16 hours. If both the taps are opened simultaneously, how long will it take to fill the tank?
(a)
(b)
(c)
(d)
24 hours
16 hours
10 hours
8 hours
(d) 83
20. Give the missing number: 5, 25, 50, 250, —, 2500.
(a) 500
(b) 750
(c) 1000
(d) 1250
21. Which one of the following numbers is exactly divisible by 9?
(a) 234
(b) 278
(c) 389
(d) 254
Department of Extension and Career Guidance
27. X goes on foot to a place at 4 kmph and returns on
a bicycle at 16 kmph. What is the average speed
of his to and fro trip?
(a)
(b)
(c)
(d)
10 kmph
8.5 kmph
6.4 kmph
5 kmph
28. 12 men working 10 hours daily complete a work in
32 days. If 30 men work in 16 days and finish the
same work, how many hours daily they worked?
(a) 5 hours
(b) 8 hours
(c) 21 hours
99
Department of Extension and Career
CHAPTER
Guidance
25. WEBSITE MODEL QUESTION PAPERS COLLECTION
(d) 12 hours
29. Ram, Shyam and hari take a contract for Rs. 550.
Ram and Shyam do 7/11 part of the work. So
hari’s share in the contract is
(a) Rs. 183.33
(c) 40
(d) 4
35. The sum of 7 numbers is 235. The last three numbers average is 45 and the first three numbers is 23
what is the value of the middle number?
(b) Rs. 200
(a) 35
(c) Rs. 300
(b) 40
(d) Rs. 400
(c) 37
30. Gopal sells two articles for Rs. 99. On one article
he losses 10% and gains 10% on the other. What
is his net gain or loss percentage?
(a) 2% loss
(b) 1% loss
(c) 2% profit
(d) 1% profit
31. If sum of money doubles itself in 16 years at simple interest, when will the same sum become three
times?
(d) 39
36. 282 − 212 = 7 × x?
(a) 7
(b) 49
(c) 343
(d) 2401
37. What is the difference of 456789 and 8999?
(a) 447790
(b) 448790
(a) 48 years
(c) 448690
(b) 32 years
(d) 447690
(c) 24 years
(d) 20 years
32. p:q=2:3, q:r=4:5 and r:s=6:7. Therefore, P:s is
equal to
(a) 4:13
38. What is the square root of 6561?
(a) 3
(b) 9
(c) 81
(d) 87
(b) 2:7
(c) 16:35
(d) 7:8
33. What is the time period, if Rs. 725 at 4% per year
simple interest accrues to Rs. 87?
(a) 5 years
39. Simplify:
(a) 1
(b) 4
(c) 8
(d) 16
(b) 4 years
(c) 3 years
(d) 2 years
34. Find x id x% of 27.5=110.
40. Evaluate:
32 + 42
.
52
(a) 5
(b) 4
(a) 4000
(c) 3
(b) 400
(d) 1
Department of Extension and Career Guidance
162 − 82 × 2
4×8
100
Department of Extension and Career Guidance
Arithmetic - Model Question Paper II
(c) 20.12
1. 6036.87÷17
(d) 16.6
(a) 358
(e) None
(b) 354.16
(c) 366.11
8. 3069+?+2935=7809
(d) 355.011
(a) 4002
(e) None
(b) 1902
(c) 1905
2. 5873+12034+1106=
(d) 1801
(a) 20001
(e) None
(b) 19016
(c) 19013
9.
16.9
× 0.169 =?
169
(d) 2018
(a) 0.0169
(e) None
(b) 0.00169
(c) 1.69
3. 25 × 15.23 =
(d) 169
(a) 386.001
(e) None
(b) 381.5115
(c) 3880.001
10. 3585+2408-1089=
(d) 3860.11
(a) 4904
(e) None
(b) 4804
(c) 5006
4. 5789-2936+1089=
(d) 9404
(a) 3942
(b) 2626
(c) 4041
(e) None
11. 333 × 693 =
(a) 220669
(d) 3932
(b) 230769
(e) None
r
?
=3
5.
9
(a) 27.8
(c) 230679
(d) 72890
(e) None
12. 66% of 40 =
(b) 520
(a) 26.40
(c) 27
(b) 28
(d) 729
(c) 24
(e) None
(d) 62.4
45
?
=
.
6.
20
?
(a) 35
(e) None
13. 256 × 270 =
(b) 30
(a) 69120
(c) 25
(b) 96120
(d) 9000
(c) 6912
(d) 59130
(e) None
(e) None
7. 81% of 22 =
(a) 1.91
(b) 19.1
Department of Extension and Career Guidance
14.
1680
× 2.5 =
25
(a) 168
101
Department of Extension and Career
CHAPTER
Guidance
25. WEBSITE MODEL QUESTION PAPERS COLLECTION
(b) 162
21.
(c) 168.1
24 × 8 − 4 × 15
=?
12 × 12 − 12
(a) 12
(d) 568
(b) 2
(e) None
(c) 16
15. 1015 ÷ 0.05 ÷ 40 =
(d) 1
(a) 50.75
(e) None
(b) 507.5
22. 2.08 − 0.52 =?
(c) 506
(a) 188
(d) 2056
(b) 1.20
(e) None
r
?
16.
=1
12
(a) 5184
(c) 4
(d) 1.83
(e) None
23. (242 − 17)2 − (7 × 5)2 =?
(b) 12
17.
(a) 49400
(c) 74
(b) 94400
(d) 144
(c) 49300
(e) None
(d) 94200
1
of 200 × 25.5=
25
(e) None
24. 44×? = 625 − 53
(a) 189
(a) 572
(b) 179
(b) 18
(c) 204
(c) 13
(d) 24.4
(d) 28
(e) None
(e) None
18. 40832-?=39053
25.
(a) 1779
5 3 7
+ + =?
4 4 6
(b) 1707
(a) 6
(c) 1877
(b) 38/72
(c) 38/12
(d) 5576
(d) 12/38
(e) None
5 3 33
=
19. × ×
1 5 10
(a) 9.09
(b) 19.9
(c) 8.09
(d) 9.9
(e) None
20. ? × 303.5 = 184983.25
(e) None
26.
6 3 4
+ + =?
5 4 5
(a) 2.075
(b) 2.75
(c) 3.75
(d) 6.70
(e) None
27. (37.5 − 0.38) + 0.04 =?
(a) 60.95
(a) 930
(b) 92112.25
(b) 922
(c) 6095
(c) 630
(d) 5678
(d) 928
(e) None
(e) None
Department of Extension and Career Guidance
102
Department of Extension and Career Guidance
28.
√
625 ÷ 0.5 =?
(b) 169
(c) 2106
(a) 50
(d) 6.23
(b) 625
(e) None
√
35. 133 − 84 ÷ (25 × 4) =?
(c) 125
(d) 12
(e) None
29. 45 + 15 +
(a) 144
(b) 17
4
=
5
5
19
19
(b)
5
18
(c)
5
(d) 18.2
(c) 71
(d) 27
(a)
(e) None
36. 27% of 320=
(a) 86.04
(b) 86.40
(c) 86.20
(e) None
√
30. 4 × 9 × 1296 =
(a) 36
(d) 86
(e) None
37. 24 + 2 × 0.25 =
(b) 1996
(a) 9.02
(c) 18
(b) 90
(d) 1296
(c) 87
(e) None
(d) 97
36 ÷ 6 − 2 × 2
31.
=?
72 − 14 × 5
(a) 2
(e) None
38. 22.8 ÷ 0.04 =
(b) 10
(a) 756
(c) 0
(b) 570
(c) 640
(d) 1
(d) 656
(e) None
32.
185 × 36
=
20
(e) None
39.
(a) 333
(a) 17
(b) 541
(b) 13.6
(c) 343
(c) 20.6
(d) 693
(e) None
√
√
625
144
33.
×
× 0.07 =
5
3
(d) 12.5
(e) None
40. 3809+? = 40.59
(a) 2.10
(a) 1.4
(b) 2.05
(b) 11.2
(c) 2.50
(c) 10.3
(d) 6.70
(d) 716
(e) None
(e) None
34. (23 × 0.05 × 4)2 =?
(a) 2612
Department of Extension and Career Guidance
5 200 20
×
÷
=
4
67
67
41.
4
3
4
+
−
=?
5 11 55
(a) 6
103
Department of Extension and Career
CHAPTER
Guidance
25. WEBSITE MODEL QUESTION PAPERS COLLECTION
(b) 55
(a) 4.07
(c) 7
(b) 9.6
(d) 0
(c) 6.8
(e) None
(d) 180
15
8
140
42. √ × √ = √
9
4
?
(e) None
47. 256 × 18 ÷ 12 =?
(a) 60
(a) 348
(b) 20
√
(c) 7
√
(d) 49
(b) 388
(c) 384
(d) 580
(e) None
(e) None
43. 1836 ÷ 18 × 12 =
(a) 1224
(b) 1205
(c) 1209
(d) 1234
(e) None
(472 − 55)2
44.
=?
23
(a) 64
18
(b) 2
23
74
(c)
23
(d) 42
(e) None
45. 18% of 2360=?
48.
√
36
400 × √ =
64
(a) 64
(b) 80
(c) 90
(d) 18
(e) None
49. 157+? + 2308 = 3500
(a) 1035
(b) 1053
(c) 1235
(d) 637
(e) None
(a) 424.8
875
50. √ = 25
?
(b) 242.8
(a) 6220
(c) 657
(b) 1225
(d) 868
(c) 1252
(e) None
(d) 7002
46. 6% of 30=?% of 200.
(e) None
Arithmetic - Model Question Paper II
1. Two trains start at the same time from Mumbai
and Chennai respectively, towards each other. After passing each other, they take 12 hours and 3
hours to reach Chennai and Mumbai respectively.
If the Mumbai Mail is moving at the speed of 48
km/h, the speed of the Chennai Mail is
(a) 24 kmph
3
2. Walking at of his normal speed, A is 16 minutes
4
late in reaching his office. The usual time taken by
him to cover the distance between his home and
his office is
(a) 48 minutes
(b) 60 minutes
(b) 22 kmph
(c) 42 minutes
(c) 21 kmph
(d) 62 minutes
(d) 96 kmph
Department of Extension and Career Guidance
3. A and B travel the same distance at the rate of
104
Department of Extension and Career Guidance
6 km per hour and 10 km per hour respectively.
If A takes 30 minutes longer than B, the distance
travelled by each is
(a) 2 kmph
(b) 3 kmph
(c) 4 kmph
(a) 6 km
(b) 10 km
(c) 7.5 km
(d) 20 km
4. Roy travels a certain distance by car at the rate of
12 km/h and walks back at the rate of 3 km/h. The
entire journey took 5 hours. Find out the distance
covered by the car.
(d) 5 kmph
9. A Maruti van takes 2 hrs. Less for a journey of
300 kilometres if its speed is increased by 5 kmph
over its usual speed. Find the usual speed of the
Maruti van.
(a) 10 kmph
(b) 12 kmph
(a) 12 km
(c) 20 kmph
(b) 30 km
(d) 25 kmph
(c) 15 km
(d) 6 km
5. Without stoppage, a bus travels a certain distance
at an average speed of 60 km/h, and with stoppage,
it covers the same distance at an average speed of
40 km/h. On an average, how many minutes per
hour does the bus stop during the journey?
10. Deba starts from a point that is on the circumference of a circle, moves 600 m towards the North
and then again moves 800 m East and reaches
a point diametrically opposite the starting point.
What is the diameter of the circle?
(a) 1000 m
(b) 500 m
(a) 20 minute per hour
(b) 15 minute per hour
(c) 10 minute per hour
(d) 5 minute per hour
6. A goes to college at a speed of 6 km/h and returns
to her home at a speed of 4 km/h. If she takes
10 hours in all, what is the distance between her
college and her home?
(a) 24 km
(b) 12 km
(c) 10 km
(d) 30 km
7. A cracked two crackers from the same place at
an interval of 12 minutes but B sitting in a bus
approaching the place hears the second report 11
minutes 30 seconds after the first. What is the approximate speed of the bus (if sound travels at the
speed of 330 metres per second)?
(a) 660/23 mps
(b) 220/7 mps
(c) 800 m
(d) 900 m
Answers:
1
6
a
a
2
7
a
c
3
8
c
c
4
9
a
d
5
10
a
a
1. It was calculated that 75 men could complete a
piece of work in 20 days. When work was scheduled to commence, it was found necessary to send
25 men to another project. How much longer will
it take to complete the work?
Answer: 30 days.
Explanation:
Before:
One day work : 1/20
One man’s one day work = 1/(20× 75).
Now:
No. of workers = 50.
One day work = 50 × 1/(20 × 75).
Total no. of days required to complete the work
= (70 × 20)/50 = 30.
(c) 330/23 mps
(d) 110/23 mps
8. A motor boat sails down the river for 10 km and
then up the river for 6 km. The speed of the river
flow is 1 km/h. What should be the minimum
speed of the motor boat for the trip to take a maximum of 4 hours?
Department of Extension and Career Guidance
2. A student divided a number by 2/3 when he required to multiply by 3/2. Calculate the percentage of error in his result.
Answer: 0%.
Explanation:
3
2
x× =x÷ .
2
3
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3. A dishonest shopkeeper professes to sell pulses at
the cost price, but he uses a false weight of 950gm.
for a kg. His gain is ...%.
Answer: 5.3%.
Explanation:
He sells 950 grams of pulses and gains 50 grams.
If he sells 100 grams of pulses then he will gain
50
× 100 = 5.26.
950
4. A software engineer has the capability of thinking
100 lines of code in five minutes and can type 100
lines of code in 10 minutes. He takes a break for
five minutes after every ten minutes. How many
lines of codes will he complete typing after an
hour?
Answer: 250 lines of codes.
5. A man was engaged on a job for 30 days on the
condition that he would get a wage of Rs. 10 for
the day he works, but he have to pay a fine of Rs.
2 for each day of his absence. If he gets Rs. 216 at
the end, he was absent for work for ... days.
Answer: 7 days.
Explanation:
The equation portraying the given problem is:
Explanation:
a percent of b : (a/100) × b
b percent of a : (b/100) × a
a percent of b divided by b percent of a :
((a/100) × b)/(b/100) × a)) = 1.
8. A man bought a horse and a cart. If he sold the
horse at 10% loss and the cart at 20 % gain, he
would not lose anything; but if he sold the horse
at 5% loss and the cart at 5% gain, he would lose
Rs. 10 in the bargain. The amount paid by him
was Rs....... for the horse and Rs........ for the cart.
Answer: C.P. of Horse = Rs. 400 and C.P.
of Cart = Rs. 200
Explanation:
Let x be the cost price of the horse and y be the
cost price of the cart.
In the first sale there is no loss or profit. (i.e.) The
loss obtained is equal to the gain.
∴ (10/100) × x = (20/100) × y ⇒ x = 2y.
In the second sale, he lost Rs. 10. (i.e.) The loss
is greater than the profit by Rs. 10.
10 × x − 2 × (30 − x) = 216
∴ (5/100) × x = (5/100) × +10.
where x is the number of working days.
Solving this we get x = 23.
Number of days he was absent was = 30-23 =7.
6. A contractor agreeing to finish a work in 150 days,
employed 75 men each working 8 hours daily. After
90 days, only 2/7 of the work was completed. Increasing the number of men by ........ each working
now for 10 hours daily, the work can be completed
in time.
Answer: 150.
Explanation:
One days work = 2/(7 × 90)
One hour’s work = 2/(7 × 90 × 8)
One man’s work = 2/(7 × 90 × 8 × 75)
The remaining work (5/7) has to be completed
within 60 days, because the total number of days
allotted for the project is 150 days.
So we get the equation
(2 × 10 × x × 60)/(7 × 90 × 8 × 75) = 5/7
where x is the number of men working after the
90th day.
Solving these two equations, we get x = 400 and
y = 200.
9. A tennis marker is trying to put together a team of
four players for a tennis tournament out of seven
available. males - a, b and c; females m, n, o and
p. All players are of equal ability and there must
be at least two males in the team. For a team of
four, all players must be able to play with each
other under the following restrictions:
• b should not play with m,
• c should not play with p, and
• a should not play with o.
Which of the following statements must be false?
(1) b and p cannot be selected together
(2) c and o cannot be selected together
(3) c and n cannot be selected together.
7. what is a percent of b divided by b percent of a?
Answer: 1.
Answer: 3
Explanation:
Since inclusion of any male player will reject a female from the team. Since there should be four
member in the team and only three males are available, the girl, n should included in the team always
irrespective of others selection.
Department of Extension and Career Guidance
106
We get x = 225.
Since we have 75 men already, it is enough to add
only 150 men.
Department of Extension and Career Guidance
10. Five farmers have 7, 9, 11, 13 & 14 apple trees,
respectively in their orchards. Last year, each of
them discovered that every tree in their own orchard bore exactly the same number of apples.
Further, if the third farmer gives one apple to the
first, and the fifth gives three to each of the second and the fourth, they would all have exactly the
same number of apples. What were the yields per
tree in the orchards of the third and fourth farmers?
Answer: 11 & 9 apples per tree.
Explanation:
Let a, b, c, d&e be the total number of apples bored
per year in A, B, C, D&Es orchard.
Given a + 1 = b + 3 = c − 1 = d + 3 = e − 6.
But the question is to find the number of apples
bored per tree in C and D s orchard.
Answer: (b)
14. The length of the side of a square is represented
by x + 2. The length of the side of an equilateral
triangle is 2x. If the square and the equilateral triangle have equal perimeter, then the value of x is
———.
Answer: x=4
Explanation:
Since the side of the square is x + 2, its perimeter
= 4(x + 2) = 4x + 8
Since the side of the equilateral triangle is 2x, its
perimeter = 3 × 2x = 6x Also, the perimeters of
both are equal.
That is 4x + 8 = 6x ⇒ x = 4.
15. (a)
If is enough to consider c − 1 = d + 3.
(b)
Since the number of trees in Cs orchard is 11 and
that of Ds orchard is 13.
(c)
Let x and y be the number of apples bored per tree
in C & d s orchard respectively.
(d)
16. (a)
Therefore 11x − 1 = 13y + 3
(b)
By trial and error method, we get the value for x
and y as 11 and 9.
(c)
(d)
11. Five boys were climbing a hill. J was following H.
R was just ahead of G. K was between G & H.
They were climbing up in a column. Who was the
second?
Answer: G.
Explanation:
The order in which they are climbing is R – G – K
–H–J
17. (a)
12. It takes Mr. Karthik y hours to complete typing
a manuscript. After 2 hours, he was called away.
What fractional part of the assignment was left incomplete?
Answer: (y-2)/y
Explanation:
To type a manuscript karthik took y hours.
(c)
Therefore his speed in typing = 1/y.
He was called away after 2 hours of typing.
(b)
(c)
(d)
18. (a)
(b)
(d)
19. (a)
(b)
(c)
(d)
20. (a)
Therefore the work completed =1/y × 2.
(b)
Therefore the remaining work to be completed =
1 - 2/y.
(c)
(i.e.) work to be completed = (y-2)/y
13. Which of the following is larger than 3/5?
(d)
21. (a)
(b)
(a) 1/2
(c)
(b) 39/50
(d)
(c) 7/25
22. (a)
(d) 3/10
(b)
(e) 59/100
(c)
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(d)
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43. (a)
(b)
(c)
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Department of Extension and Career Guidance
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(b)
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(b)
(c)
(d)
67. (a)
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(c)
Department of Extension and Career Guidance
(d)
68. (a)
(b)
(c)
(d)
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