Percentages and Ratio: Practice Set 5
Percentages and Ratio: Practice Set 5 is a mixed practice set pairing percentage and ratio questions: percentage of an amount, percentage change, simplifying ratios, and sharing an amount in a ratio. Papers combine these two skills often because both rely on proportional reasoning, and moving between them (for example, turning a ratio into a percentage) is a common 11+ question type.
Before you start
Make sure you're comfortable with these topics first:
Method
- Decide first whether a question is a percentage question or a ratio question, since they use different starting steps.
- For a percentage-of-an-amount question, find 10% first, then build the required percentage from it by halving, doubling or adding.
- For a percentage change question, decide whether it is an increase or a decrease, then either adjust the amount directly or use a single multiplier, for example +15% is x1.15.
- For a ratio question, always simplify the ratio first by dividing every part by their highest common factor.
- To share an amount in a ratio, add the parts to find the total number of parts, divide the amount by this total, then multiply by each part.
- For a question linking percentage and ratio, convert one to the other, for example turning 'in the ratio 3:2' into 3/5 and 2/5, or 60% and 40%.
- Check any ratio or percentage answer by confirming the parts recombine to the original total, or to 100%.
Worked example
A prize fund of £240 is shared between two winners in the ratio 5:3. What percentage of the total does the winner with the larger share receive?
- Add the ratio parts: 5 + 3 = 8.
- Find the value of one part: 240 / 8 = 30.
- Find the larger share: 5 x 30 = 150.
- Express the larger share as a fraction of the total: 150/240.
- Convert this fraction to a percentage: 150/240 = 0.625 = 62.5%.
Practice questions
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Q1Find 30% of 150.Show answer
Answer: 45 (10% is 15, so 15 x 3 = 45)
Q2Simplify the ratio 18:24.Show answer
Answer: 3:4
Q3Share £60 in the ratio 2:3:5.Show answer
Answer: Total parts = 10, one part = 6, shares are £12, £18 and £30.
Q4A shirt costs £25 and is reduced by 20%. Find the new price.Show answer
Answer: 20% of 25 = 5, so 25 - 5 = £20.
Q5Express the ratio 15:25 in its simplest form.Show answer
Answer: 3:5
Q6Increase 80 by 25%.Show answer
Answer: 25% of 80 = 20, so 80 + 20 = 100.
Q7A class has 12 boys and 18 girls. Write the ratio of boys to girls in its simplest form.Show answer
Answer: 12:18 = 2:3
Q8Find 45% of 200.Show answer
Answer: 90 (10% is 20, so 4 x 20 = 80, plus 5% which is 10, giving 90)
Exam-style questions
Written in the style of a 11+ exam paper, with a full mark scheme.
In a school of 300 students, the ratio of students who walk to school to those who do not is 2:3. (a) How many students walk to school? (b) What percentage of the school walks to school?
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A jacket originally costs £80. It is first reduced by 25% in a sale, then a further 10% is taken off the sale price. (a) Find the price after the first reduction. (b) Find the final price after the second reduction.
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Free printable worksheet
Want more practice on paper? Download the percentages and ratio: practice set 5 worksheet pack - 10 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 38 of 11+ Maths Workbook 1, the whole course as one free printable PDF.
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