Percentages: Practice Set 3
Percentages: Practice Set 3 gives further practice at applying a single percentage change using a multiplier, expressing one amount as a percentage of another, and combining two percentage changes applied one after another. It follows on from the two earlier Percentages sets and builds towards reverse percentage problems.
Method
- To apply a percentage increase using a multiplier, add the percentage, as a decimal, to 1, so a 12% increase means multiplying by 1.12.
- To apply a percentage decrease using a multiplier, subtract the percentage, as a decimal, from 1, so a 12% decrease means multiplying by 0.88.
- To express one amount as a percentage of another, write the first amount as a fraction of the second, then multiply by 100.
- For two percentage changes applied one after another, apply the first multiplier to the original amount, then apply the second multiplier to that result, never to the original amount again.
- To find a single multiplier equivalent to two combined percentage changes, multiply the two individual multipliers together.
- Check whether a combined change of, say, a 10% increase followed by a 10% decrease returns you to the original amount; it does not, because the second change is applied to a different amount than the first.
Worked example
A price of 90 pounds is increased by 8%, and then the new price is decreased by 5%. Find the final price.
- Apply the 8% increase using a multiplier: 90 x 1.08.
- Work out 90 x 1.08 = 97.20 pounds.
- Apply the 5% decrease to this new price using a multiplier: 97.20 x 0.95.
- Work out 97.20 x 0.95 = 92.34.
- The final price is 92.34 pounds.
Practice questions
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Q1Increase 150 by 12%.Show answer
Answer: 168 (150 x 1.12)
Q2Decrease 240 by 15%.Show answer
Answer: 204 (240 x 0.85)
Q3Express 18 out of 40 as a percentage.Show answer
Answer: 45% (18/40 = 0.45)
Q4A price of 60 pounds is increased by 10%, then the new price is increased by a further 10%. Find the final price.Show answer
Answer: 72.60 pounds (60 x 1.1 = 66, then 66 x 1.1 = 72.60)
Q5A quantity is decreased by 20%, then decreased again by 25%. Find the single decimal multiplier equivalent to both changes combined.Show answer
Answer: 0.6 (0.8 x 0.75), equivalent to a single 40% decrease
Q6Out of 25 questions in a test, Sam gets 21 correct. What percentage did Sam get correct?Show answer
Answer: 84% (21/25 = 0.84)
Exam-style questions
Written in the style of a 11+ exam paper, with a full mark scheme.
Increase 45 pounds by 8%, showing your method.
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In a survey of 80 pupils, 52 own a bicycle. (a) Calculate the percentage of pupils who own a bicycle. (b) The following year, 60 out of the same 80 pupils own a bicycle. Calculate how many more pupils own a bicycle compared with the first survey, and state the new percentage.
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A washing machine originally costs 320 pounds. In a sale, the price is reduced by 15%. A store loyalty card then gives a further 5% off the sale price. (a) Calculate the price after the first reduction. (b) Calculate the final price after both reductions. (c) Calculate the single percentage discount that is equivalent to both reductions combined.
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Free printable worksheet
Want more practice on paper? Download the percentages: practice set 3 worksheet pack - 9 pages of exam-style questions with a full mark scheme. One email opens every download in this browser for 14 days - no account, no card. Print it for personal and classroom use.
This topic is chapter 34 of 11+ Maths Workbook 1, the whole course as one free printable PDF.
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