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Percentage calculations
It is important that you are able to work with percentages confidently. Ideas such as
percentage change are often used in areas such as data handling.
This worksheet explores some of the calculations that you might be expected to perform.
Interpreting numerical answers is also important, and some of the following questions
require you to do this.
Simple percentages
1. Three batches of electrical resistors are analysed for defects.
Batch 1. Out of 235 resistors, 12 are found to be substandard.
Batch 2. Out of 470 resistors, 17 are found to be substandard.
Batch 3. Out of 711 resistors, 29 are found to be substandard.
Calculate the percentage of substandard resistors in each batch.
Quality control requires that no more than 5% of resistors are substandard. Which
batches, if any, fail to meet this requirement?
2. 20% of a group of new maths students at a college are asked to comment on the
effectiveness of their induction process. If there are 375 such students, how many will
be asked?
3. In a random sample of 62 businesses in Huddersfield, 9 reported that their sales had
significantly dropped over the last year. In Bristol, in the south of England, 18% of
similar businesses reported the same results.
Using this evidence, comment on the view that the recession has affected the north of
England more seriously than the nouth.
Percentage change
1. An antique Moorcroft vase increased in value from £240 in 1988 to £855 in 2005.
Calculate the percentage increase.
2. Hashima, a coal-mining island in Japan, experienced a huge increase in population in
the period after the Second World War.
In 1950, the population was 862. In 1952, the population was 3,243.
By way of contrast, the population of Huddersfield increased from 105,140 to 110,306
in the same period.
a. Calculate the increase in population of both Hashima and Huddersfield.
b. Calculate the percentage increase for the two places.
c. In which location do you think the effect of the population rise was more significant?
Explain your answer.
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Hashima Island, Japan
3. Two computer stores recorded the mean weekly number of tablet devices sold before
and after they conducted advertising campaigns.
Store A experienced growth from 27 to 34 devices.
Store B experienced growth from 40 to 51 devices.
Calculate the percentage increase for each store. Which advertising campaign
appears to have been more successful?
Reverse percentages
This is where you are told the value of something after it has been changed by a certain
amount.
1. A Sports Studies student has trained hard for the 400m. Her personal best time after
training is 62.4 seconds, which is a reduction of 6% on her previous best. What was
her previous best time?
2. The mean price for a one-bedroom flat in Mayfair rose by 3.2% during 2012. At the
end of 2012 the mean price was £425,000. Find the amount by which the mean price
rose during 2012.
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Mixed questions
Here are some mixed questions for you to try.
1. Infant mortality data for three different countries are given in the table below. The GDP
figure is one measure of the economic prosperity of the country. The mortality figures
are deaths per 1000; the GDP figures are mean values over the period 1980 to 2010,
in US$ per person.
Country
GDP
Mortality, 1980
Mortality, 2010
Norway
62767
6.42
2.48
Brazil
11909
52.4
23.5
Tanzania
340.20
106.8
62.4
a. Calculate the percentage change in the infant mortality for the three countries.
b. Comment on the claim that the success of measures to reduce infant mortality
depends on the economic prosperity of the country.
2. A college is trying to increase the number of girls taking Level 3 courses in maths and
science by outreach work with local feeder schools.
Before the work, 28% of students on maths and science courses were female. In the
current intake, 190 of the total number of 545 students choosing maths or science are
female.
a. Calculate the percentage of the new intake choosing maths or science who are
female.
b. The college had set a target of 40% of such students being female. How many of
the intake of 545 students would they have needed to reach this target?
3. A Core Maths student is investigating how well people can estimate distances. Two
students, Sarah and Arfan, estimate the length of the college’s study centre to be 15m
and 23m, respectively. The actual length is 21.4m. Calculate the percentage errors of
the students, and state which one was more accurate.
4. An environmental pressure group has persuaded a local industry to change the way
they operate. Fishermen report that 28 pike have been caught in a pond during the
last year, into which the industry had previously deposited waste. If this represents a
40% increase, calculate the number of pike caught previously.
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