Ratio and Proportion: Practice Set 3
Ratio and Proportion: Practice Set 3 is a third practice round for 11+ ratio and proportion, moving from simplifying and sharing ratios towards multi-step problems that combine ratio with percentages, fractions and a difference in shares within a single question.
Before you start
Make sure you're comfortable with these topics first:
Method
- Before starting a ratio calculation, check whether the question has given you a total, a difference or a single share, since each type needs a different first step.
- To share a total in a given ratio, add the parts to find the total number of parts, divide the total by this number to find one part, then multiply to find each share.
- When you are given a difference between two shares, find the value of one 'gap' part first, then scale up to find the total or the individual shares.
- To compare or combine two ratios, write both using a common shared term so they can be merged into a single ratio or compared directly.
- In problems that combine ratio with fractions or percentages, convert the fraction or percentage to a matching ratio (or the ratio to a fraction) before combining the two pieces of information.
- Always check a final ratio answer is in its simplest form by dividing every part by their highest common factor.
Worked example
A charity fun run raises money split between two charities, A and B, in the ratio 7 : 5. Charity A receives 63 pounds more than charity B. Work out the total amount raised.
- Find the difference in parts of the ratio: 7 - 5 = 2.
- Divide the difference in amounts by this number of parts to find the value of one part: 63 / 2 = 31.50 pounds.
- Add the parts of the ratio to find the total number of parts: 7 + 5 = 12.
- Multiply the unit value by the total number of parts to find the total amount raised: 12 x 31.50 = 378 pounds.
- Final answer: 378 pounds.
Practice questions
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Q1Simplify the ratio 45 : 60 to its simplest form.Show answer
Answer: 3 : 4
Q2A drink is made from concentrate and water in the ratio 1 : 4. How many millilitres of water are needed for 30 ml of concentrate?Show answer
Answer: 120 ml (4 x 30 = 120)
Q3Complete the missing number: 9 : 4 = ___ : 20.Show answer
Answer: 45
Q4A sum of money is shared between Leo and Zara in the ratio 3 : 7. Zara receives 84 pounds more than Leo. How much does Leo receive?Show answer
Answer: 63 pounds (84 / 4 = 21, 21 x 3 = 63)
Q5The ratio of cars to vans in a car park is 5 : 2. There are 40 cars. How many vehicles are there in total?Show answer
Answer: 56 (40 / 5 = 8, 8 x 2 = 16 vans, 40 + 16 = 56)
Q6A model plane is built to a scale of 1 : 48. The wingspan of the real plane is 14.4 m. Calculate the wingspan of the model, in centimetres.Show answer
Answer: 30 cm (14.4 m = 1440 cm, 1440 / 48 = 30)
Exam-style questions
Written in the style of a 11+ exam paper, with a full mark scheme.
The ratio of red to blue counters in a bag is 5 : 3. Calculate what percentage of the counters are blue.
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A sum of 150 pounds is shared between three friends, Dan, Ella and Faye, in the ratio 4 : 5 : 6. Calculate how much more Faye receives than Dan.
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In a school, the ratio of Year 5 to Year 6 pupils is 6 : 5, and the ratio of Year 6 to Year 7 pupils is 3 : 4. Express the ratio of Year 5 to Year 6 to Year 7 pupils in its simplest form.
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Free printable worksheet
Want more practice on paper? Download the ratio and proportion: practice set 3 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 4 of 11+ Maths Workbook 2, the whole course as one free printable PDF.
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