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INFANT JESUS GROUP OF ENGINEERING COLLEGES
PLACEMENT TRAINING – QUANTITATIVE APTITUDE
RATIO AND PROPORTION
a
.
b

a : b represents the fraction

The multiplication or division of each term of a ratio by a nonzero number does not affect the
ratio.

The equality of two ratios is called proportion.
It is written as a: b = c: d or a: b:: c : d. Here, the first and fourth terms are called extremes while
the second and third terms are called means.

In a proportion, product of extremes = product of means. i.e. ad = bc.

If
a c
ab cd ab cd ab cd
 then

,

,

b d
b
d
b
d a b c d
PROBLEMS
1. The ratio 4
a) 4 : 1
3.5
: 25 is the same as
b) 2 : 1
c) 7 : 5
d) 7 : 10
Answer: a) 4 : 1
Solution: 4
3.5
: 2 5 = 27 : 25 = 2 2 : 1
2. Two whole numbers whose sum is 64 cannot be in the ratio:
a) 5 : 3
b) 7 : 1
c) 3 : 4
d) 9 : 7
Answer: c) 3 : 4
Solution: 3 + 4 does not divide 64.
In all the other cases, the sum divides 64
3.
If
x 8
 then 5x – 4y : 3x + 2y is
y 9
a) 21 : 2
b) 21 : 13
c) 2 : 21
d) 13 : 21
Answer: c) 2 : 21
(
Solution:
=(
) (
) (
)
)
=
=
4. Three friends divide Rs.624 in the ratio
=
1 1 1
: : .
2 3 4
The share of the third friend is
a) Rs.288
b) Rs.192
c) Rs.148
d) Rs.144
Answer: d) Rs.144
Solution:1/2 : 1/3 : 1/4 = 6 : 4 : 3
× 624 = 144
The share of the third friend =
5. if A : B = 2 : 3 and B : C = 4 : 5 then C : A is
a) 15 : 8
b) 12 : 10
c) 8 : 5
d) 8 : 15
Answer: a) 15 : 8
Solution:A : B : C
2:3
4:5
8 : 12
12 : 15 by standardizing the middle ratio
8: 12 : 15
A walks 5
4
1
11
1
Km in 2 hrs. B walks
Km in 11 mins. What is the ratio of their speeds?
9
3
16
4
a) 24 : 25
b) 11 : 7
Answer: c) 7 : 11
Solution:
:
;
×
c) 7 : 11
:
×
×
= 7 : 11
d) 24 : 13
6. A bag contains 50 paise, 25 paise and 10 paise coins in the ratio 5: 9: 4 amounting to Rs.206. The
number of 25 paise coins is
a) 200
b) 360
c) 160
d) 260
Answer: b) 360
Solution: The number of 25 paise coins must be a multiple of 9.
The only multiple of 9 in the given answers is 360
7. If a + b : b + c : c + a = 6 : 7 : 8 and a + b + c = 14 then the value of c is
a) 7
b) 2
c) 6
d) 8
Answer: c) 6
Solution: Let a + b=6k
a+b = 6k; b + c =7k, c + a =8k;
Adding, 2 (a + b + c) = 21 k
k=
=
c = (a + b + c) – (a + b) = 14 – (6 x ) = 6
8. An amount of Rs.2430 is divided among A, B, C such that if their shares be reduced by Rs.5,
Rs.10 and Rs.15 respectively, the remainders shall be in the ratio 3: 4: 5. The share of B is
a) Rs.605
b) Rs.790
c) Rs.800
d) Rs.810
Answer: d) Rs.810
Solution:
Amount after reducing = 2430-(5+10+15)= 2400
Ratio of shares 3 : 4 : 5 => 12 k = 2400; k = 200
Share of B= 4 k + 10 = 810
9. The sum of three numbers is 98. If the ratio of the first to the second is 2 : 3 and that of the
second to the third is 5 : 8 then the second number is
a) 20
b) 30
c) 48
d) 58
Answer : b) 30
Solution:
F :S:T
2:3
5:8
10 : 15 : 24
49 k = 98; k = 2; 15K = 30
10. If three numbers in the ratio 3 : 2 : 5 be such that the sum of their squares is 1862, the middle
number will be
a) 7
b) 14
c) 21
d) 35
Answer: b) 14
Solution:
(9 + 4 + 25 )k2=1862 , if the numbers are 3k, 2k , 5k
38k2 = 1862; k2 = 49;
k = 7;
2k =14
11. In a school 10% of the boys are same in number as 1/4th of the girls and 10% of the girls are same
in number as 1/25th of the boys. What is the ratio of boys to girls in that school?
a) 3 : 2
b) 5 : 2
c) 2 : 1
d) 4 : 3
Answer: b) 5: 2
Solution:
10% of the boys = (
)B= ;
=
=
We don’t need the other conditionat all.
12. The incomes of A, B, C are in the ratio of 7: 9: 12 and their spending are in the ratio of 8: 9: 15.
If A saves 1/4th of his income, then the savings of A, B, C are in the ratio of
a) 56: 99: 69 b) 99: 56: 69
c) 69: 56: 99
d) 99: 69: 56
Answer: a) 56: 99: 69
Solution:
Incomes be 7x, 9x,12x
Spending be 8y,9y,15y
Savings will be 7x -8y, 9x – 9y, 12x- 15y
The middle part has to be a multiple of 9,
This is the only option.
13. Ramana divides two sums of money among his four sons Ganesh, Mahesh, Anil and Sunil. The
first sum is divided in the ratio 4: 3: 2: 1 and second in the ratio 5: 6: 7: 8. If the second sum is
twice the first, the largest total is received by
a) Ganesh
b) Mahesh
c) Anil
d) Sunil
Answer: a) Ganesh
Solution:
Let the first sum be 4x, 3x, 2x, x
Second sum be 5y, 6y, 7y, 8y
The second sum is twice the first sum
26y = 20x; 13y = 10x
Take y=10 x= 13
G:M:A:S
4X+5Y: 3X+6Y: 2X +7Y: X+8Y
102: 99: 96: 93
14. 20 litres of a mixture contains milk and water in the ratio 5: 3. If 4 litres of this mixture are
replaced by 4 litres of milk, the ratio of milk to water in the new mixture will become
a) 2 : 1
b) 7 : 3
c) 8 : 3
d) 4 : 3
Answer: b)7: 3
Solution:
M: W
5: 3
After 4 litres of mixture removed also the ratio remains the same.
The contents will be 10litres milk and 6litres water.
After 4 litres of milk added, the ratio is 14: 6 = 7: 3
15. Aand B are two alloys of gold and copper prepared by mixing metals in the ratio 7: 2 and 7: 11
respectively. If equal quantities of the alloys are melted to form a third alloy C, the ratio of gold
and copper in C will be
a) 5 : 9
b) 5 : 7
c) 7 : 5
d) 9 : 5
Answer: c) 7: 5
Solution:
9kg of A contains 7G, 2C
18Kg of B contains 7G, 11C
Take 18kg of A and 18kg of B
We get 21G, 15C
7: 5
16. A mixture contains milk and water in the ratio 5: 1. On adding 5 litres of water, the ratio of milk
to water becomes 5: 2. The quantity of milk in the original mixture is :
a) 16 litres
b) 25 litres
c) 22.75 litres d) 32.5 litres
Answer: b) 25 litres
Solution:
M: W
5k: k
5litres of water is added.
5k : k+5 =5 : 2
10k = 5k +25; k =5
The quantity of milk in the original mixture= 5k= 25
17. Two equal glasses are respectively
1
1
and full of milk. They are then filled with water and the
3
4
contents mixed in a tumbler. The ratio of milk and water in the tumbler is :
a) 7 : 5
b) 7 : 17
c) 9 : 21
d) 11 : 23
Answer: b) 7: 17
Solution:
m:w
+ ∶ +
4+3 : 8+9
7:17
(multiplying by 12)
18. If A : B = 3 : 4 and B : C = 8 : 9 then A : C is equal to
a) 1 : 3
b) 3 : 1
c) 2 : 3
d) 3 : 2
Answer c) 2 : 3
Solution:
\
A : B :C
3 :4
8 :9
6 : 8 : 9TAKING lcm for B ratio’s and multiplying the ratios suitably
A : C IS 6 :9 , 2:3
19. If A : B = 5 : 7 and B : C = 6 : 11 then A : B : C is
a) 55: 77: 66 b) 30: 42: 77 c) 35: 49: 42
d) none of these
Answer: b) 30: 42: 77
Solution:
A:B:C
5:7
6 :11
30 : 42 : 77TAKING lcm for B ratio’s and multiplying the ratios suitably
20. Two numbers are in the ratio 3: 5. If each number is increased by 10, the ratio becomes 5: 7. The
numbers are
a) 3, 5
b) 7, 9
c) 13, 22
d) 15, 25
Answer: d) 15, 25
Solution:
Let the numbers be 3k, 5k
After increasing by 10,
3k + 10 : 5k +10 = 5 :7
4k =20, k=5
The numbers are 15, 25
21. The speeds of three cars are in the ratio 3: 4: 5. The ratio between times taken by them to travel
the same distance is
a) 3: 4: 5
b) 5: 4: 3
c) 12: 15: 20 d) 20: 15: 12
Answer:d) 20: 15: 12
Solution:
Ratio of speeds is 3 : 4 : 5
Ratio of times is 1/3 :1/4 : 1/5
20: 15:12 multiplying by the lcm 60
22. 94 is divided into two parts in such a way that fifth part of the first and eighth part of the second
are in the ratio 3 : 4. The first part is
a) 27
b) 30
c) 36
d) 48
Answer: b) 30
Solution:
F/5: S/8 = 3: 4
4F / 5 = 3S /8
32 F =15S
F: S = 15:32
30:64 to make the sum 94
23. Divide Rs.171 into two parts whose ratio will be 9:10.
a) 56, 115
b) 81, 90
c) 63, 108
d) 108, 63
Answer: b) 81, 90
Solution:
19k = 171
K=9
The amounts will be 9k, 10k
81,90
24. Find the ratio of 2.5 litre to 750ml.
a) 3 : 10
b) 3 : 4
c) 10 : 3
d) 12 : 13
Answer:c) 10 : 3
Solution:
ratio of 2.5 litre to 750ml is 2500/ 750 =10/3
25. If 2A = 3B = 4C, then A : B : C is
a) 2: 3: 4
b) 4 : 3 : 2
c) 6 : 4 : 3
d) 3 : 4 : 6
Answer: c) 6 : 4: 3
Solution:A/B = 3/2 , B/C =4/3
A :B :C
3 :2
4 :3
6 : 4 :3TAKING lcm for B ratio’s and multiplying the ratios suitably
a b c
a bc
  then
is equal to
3 4 7
c
1
a) 7
b) 2
c)
2
26. If
Answer: b) 2
Solution:
= = =
=
;
=
d)
1
7
27. Five bananas and four apples cost as much as 3 bananas and 7 apples. The ratio of the cost of one
banana to that of one apple is
a) 3 : 2
b) 4 : 3
c) 3 : 4
d) 1 : 3
Answer:a) 3: 2
Solution:
5B + 4A =3B+ 7A
2B = 3A;
=
28. The ratio of income of A to that of B is 5: 4 and the expenditure of A to that of B is 3: 2. If at the
end of the year, each saves Rs.800, the income of A is
a) Rs.1600
b) Rs.1800
c) Rs.2000
d) Rs.2200
Answer: c) Rs.2000
Solution:
Income - expenditure for A is 5x – 3y
Income - expenditure for B is 4x – 2y
5x – 3y = 800; 4x – 2y = 800
Subtracting x –y =0; x = y
2x =800; x =400; 5x =2000
29. Rs.53 is divided among A, B, C such that A’s share is Rs.7 more than B’s share and B’s share is
Rs.8 more than C’s share. The ratio of their shares is
a) 16: 9: 18
b) 25: 18: 10 c) 18: 25: 10 d) 15: 8: 30
Answer: b) 25: 18: 10
Solution:
A = B +7, B = C+8
A + B + C =53
(B+7) +B+ (B-8) =53
B = 18
A:B:C = 25 :18:10
30. 85 Kg of a mixture contains milk and water in the ratio 27: 7. How much more water is to be
added to get a mixture containing milk and water in the ratio 3 : 1.
a) 5Kg
b) 6.5Kg
c) 7.25Kg
d) 8 Kg
Answer: a) 5Kg
Solution:
M :W
27 :7
67 ½ : 17 ½ Multiplying by 2 ½ to make the sum 85
67 ½ : 17 ½ + x adding x kg of water
67 ½ : 17 ½ + x = 3:1
67 ½ = 52 ½ + 3x; x = 5
31. Two numbers are in the ratio of 3: 5. If 9 be subtracted from each, they are in the ratio of 12: 23.
The first number is
a) 27
b) 33
c) 55
d) 49
e) none of these
Answer:b) 33
Solution:
3x -9 : 5x -9 = 12 :23
69x- [9 x 23] = 60x – [ 9 x 12]
9x = 99; 3x=11; 3x = 33
32. If A : B = 2 : 3, B : C = 4 : 5 and C : D = 3 : 7 then A : B : C : D is
a) 2 : 4 : 3 : 7 b) 2 : 12 : 15 : 7 c) 8 : 12 : 15 : 35d) 8 : 12 : 16 : 35
Answer:
Solution:
c) 8 : 12 : 15 : 35
A:B:C:D
2:3
4:5
8:12:15
3:7
8 : 12 : 15 : 35
33. Two numbers are such that their difference, their sum and their product are in the ratio 1: 7: 24.
The product of the numbers is
a) 6
b) 12
c) 24
d) 48
Answer: d) 48
Solution:
a-b :a+b :ab
1: 7 : 24
(a+b)2 – (a-b)2 = 4ab; (7k)2 – k2 = 4 × 24k
k=2; 24k =48
35. The ratio of number of males to number of females in a club is 7: 4. If there are 84 males in the
club, the total number of members in the club is
a) 126
b) 132
c) 136
d) 148
Answer: b) 132
Solution:
M:F
7:4
84 : 48,multiplying by 12
The total number is 84+48
36. A map is drawn on the scale of 4mm for each 16Km. Two places are shown on the map at a
distance of 7.2mm. How far away they are from each other?
a) 22.3Km
b) 9.21Km
c) 28.8Km
d) 21.8Km
Answer: c) 28.8Km
Solution:
4mm => 16km
7.2 mm => x 7.2 = 28.8 km
37. The ratio of two numbers is 3: 8 and their difference is 115. The greater number is
a) 69
b) 184
c) 230
d) 240
Answer:b) 184
Solution:
S:G
3: 8
3k , 8k and the difference is 5k
5k = 115, k=23
The greater number is 8k= 184
38. If
a 2
b 4
ab
 and  then
is
b 3
c 5
bc
a) 5 : 9
b) 8 : 15
Answer:c) 20 : 27
Solution:
=
c) 20 : 27
=>
multiplying
39. If 3x = 8y and 5y = 9z then
a)
72
15
Answer: a)
b)
83
15
=
d) 27 : 20
= ; =
=
=>
=
=
=
x
is
z
c)
9
8
d)
11
83
72
15
Solution:
= , =
Multiplying, =
=
40. The marks obtained by Suresh in English, Maths and Science are in the ratio
total score is 860, his marks in English is
a) 160
b) 228
c) 312
Answer: d) 300
Solution:
E:M:S
1/2 ; 1/3 : 3/5
d) 300
1 1 3
: : . If his
2 3 5
15 : 10 : 18, multiplying by 30
43 k = 860; k= 20
Marks in English = 15k = 300
41. Solve 2x + 1 : x + 5 = 6x – 7 : 3x + 5
a) 8
b) 4
c) 6
Answer:b) 4
Solution:
d) 2
(2x + 1) (3x + 5 ) = ( x + 5 ) ( 6x -7 )
In both sides we get 6x2
Hence 13x + 5 = 23x – 35
10x = 40; x = 4
42. What number should be subtracted from both the terms of the ratio 15:19 to make it as 3: 4?
a) 3
b) 5
c) 6
d) 9
Answer: a)3
Solution:
15-x: 19 – x = 3:4
60- 4x = 57 – 3x; x = 3
43. The average age of three boys is 25 years and their ages are in the ratio 3: 5: 7. The age of the
youngest boy is
a) 21 years
b) 18 years
c) 15 years
d) 9 years
Answer:c) 15 years
Solution:
average age = 25
Sum of their ages = 75
15k= 75; k=5
Age of the youngest boy = 3k = 15
44. X, Y and Z share a sum of money in the ratio 7: 8: 16. If z receives Rs.27 more than X then the
total money shared was
a) Rs.48
b) Rs.93
c) Rs.279
d) Rs.558
Answer: b) Rs.93
Solution:
Z receives 27 more than x
16k – 7k = 27
9k = 27; k =3
Total money = (7+8+16)k = 93
45. Rs.1870 is divided into three parts in such a way that half of the first part, one-third of the second
part and one-sixth of the third part are equal. The third part is
a) Rs.510
b) Rs.680
c) Rs.850
d) Rs.1020
Answer:d) Rs.1020
Solution:
F/2 = S/3= T/6
T = 2S = 3F
F + S + T = 1870
T( 1/3 +1/2 + 1 ) = 1870
T= 1870 x = 170 x 6 = 1020
Or the third part is a multiple of 6 and is large
46. A 24 litres mixture contains water and milk in the ratio 3: 5. How much water should be added to
this mixture to reverse this ratio?
a) 10
b) 12
c) 15
d) 16
Answer:d) 16
Solution:
W:M
3: 5
9 :15 to make the sum 24
9 + x : 15 = 5 : 3
27 + 3x = 75; x = 16
47. The diameters of the fore wheel and the rear wheel of a tractor are in the ratio 1: 4. When the
fore wheel makes 100 revolutions per minute, how many revolutions per minute would the rear
wheel make?
a) 18
b) 23
c) 25
d) 17
Answer: c) 25
Solution:
ratio of diameters1 : 4
Ratio of circumferences 1: 4
Ratio of revolution 1 :1/4
4: 1
100 : 25
48. A business man prints two types of prices on his goods; one is for cash payment and other for
those who pay after one month. If the rate of interest is 12% then the two prices are in the ratio
a)
100
101
Answer: a)
Solution:
b)
101
100
c)
50
51
d)
51
50
100
101
Rate of interest 12 % means interest for Rs100 for 1 year is 12 Rs
Interest for Rs.100 for 1 month is Re1
The ratio is 100 : 101
3
3
49. If a : b  216 : 512 then
a) 6
ab
is
ab
b) 7
c) -7
d) -6
Answer: c) -7
Solution:
a3/ b3 =
= 63 / 83
a/b = 6/8
=
,
=
(
)
= -7
50. In a factory men, women and children were employed in the ratio 8:5:1to finish a job and their
individual wages were in the ratio 5:2:3. Total daily wages of all amount to Rs.318. Find the total
daily wages paid to each category.
a)Rs.240,60,18
b)Rs.210,70,38
c)Rs.190,95,33
d)none of these
Answer:a) Rs.240,60,18
Solution:
M:W:C
8:5:1
Individual wages
5:2:3
Category wages 8x5 : 5x2 : 1x3
40 : 10 : 3
53k = 318g
Total daily wages paid to each category Rs.240,60,18