Ratio and Proportion: Practice Set 4
Ratio and Proportion: Practice Set 4 is a fourth practice round for 11+ ratio and proportion, pushing into the hardest multi-step questions on real papers, where a ratio changes after a group grows or shrinks and several linked calculations are needed to reach the final answer.
Before you start
Make sure you're comfortable with these topics first:
Method
- Read the whole question before starting, since a Practice Set 4 ratio question often needs two or three linked calculations rather than a single share.
- Identify what kind of information you have been given, a total, a difference, a single share or a change to one group, and choose the matching method for that first step.
- Work systematically through multi-part questions, writing down each intermediate result clearly so it can be reused in a later part.
- When a ratio changes because one group grows or shrinks by a fixed amount or a percentage, recalculate that group's new value before writing the new ratio.
- To convert a ratio to a fraction or a percentage of the whole, put the relevant part over the total number of parts.
- Check every answer by substituting it back into the original ratio or total to confirm it stays consistent.
Worked example
A youth club has members split between Juniors and Seniors in the ratio 5 : 3. There are 40 Juniors. If 8 more Seniors join and no Juniors leave, work out the new ratio of Juniors to Seniors in its simplest form.
- Find the value of one part using the Juniors: 40 / 5 = 8.
- Find the original number of Seniors: 3 x 8 = 24.
- Add the new Seniors who join: 24 + 8 = 32.
- Write the new ratio of Juniors to Seniors: 40 : 32.
- Simplify by dividing both parts by their highest common factor, 8: 5 : 4.
Practice questions
Type your answer and press Check to be marked straight away, or reveal the answer and mark yourself.
Q1Simplify the ratio 63 : 81 to its simplest form.Show answer
Answer: 7 : 9
Q2An allotment plot has vegetables and flowers in the ratio 7 : 3. There are 21 vegetable plants. How many flower plants are there?Show answer
Answer: 9 (21 / 7 = 3, 3 x 3 = 9)
Q3Complete the missing number: 8 : 15 = 40 : ___.Show answer
Answer: 75
Q4A sum of money is shared between two charities in the ratio 9 : 11. The smaller share is 108 pounds. Work out the total amount shared.Show answer
Answer: 240 pounds (108 / 9 = 12, 12 x 20 = 240)
Q5The ratio of cats to dogs at a shelter is 4 : 9. There are 65 animals in total. How many dogs are there?Show answer
Answer: 45 (65 / 13 = 5, 5 x 9 = 45)
Q6A rope is cut into two pieces in the ratio 5 : 8. The shorter piece is 1.75 m long. Calculate the length of the longer piece.Show answer
Answer: 2.8 m (1.75 / 5 = 0.35, 0.35 x 8 = 2.8)
Exam-style questions
Written in the style of a 11+ exam paper, with a full mark scheme.
A fruit squash is made from concentrate and water in the ratio 2 : 9. Calculate what percentage of the mixture is concentrate, giving your answer to 1 decimal place.
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A company has employees split between two departments, Sales and Support, in the ratio 7 : 5. There are 30 more Sales employees than Support employees. The company then hires 20 new Support employees, with no change in Sales. Calculate the new ratio of Sales to Support employees in its simplest form.
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In a garden centre, the ratio of trees to shrubs is 3 : 8, and the ratio of shrubs to flowers is 4 : 5. There are 96 shrubs. Calculate the total number of trees, shrubs and flowers.
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Free printable worksheet
Want more practice on paper? Download the ratio and proportion: practice set 4 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 5 of 11+ Maths Workbook 2, the whole course as one free printable PDF.
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