Ratio and Proportion Depth
Ratio and Proportion Depth extends basic ratio and proportion work to harder question types: three-part ratios, ratio problems given the difference between shares rather than the total, combining ratio with fractions, and direct proportion reasoning where a scale factor must be found and applied. These formats are common in the reasoning-heavy sections of GL Assessment and CEM papers.
Method
- Identify whether a ratio problem gives the total amount, the difference between shares, or one share's exact value, since each type needs a different first step.
- For a ratio given as a total, find the value of one part by dividing the total by the sum of the ratio parts, then multiply to find each share.
- For a ratio given as a difference, find the value of one part by dividing the difference by the difference between the ratio numbers.
- For a three-part ratio, use the same method as a two-part ratio but divide by the sum of all three parts.
- For proportion problems, decide whether the relationship is direct, both quantities increasing together, or inverse, before setting up the calculation.
- Convert a ratio to a fraction of the whole, for example 2:3 means 2/5 and 3/5, when a question asks for a share expressed as a fraction or percentage.
Worked example
Two brothers share some money in the ratio 3:5. The elder brother receives 24 pounds more than the younger brother. How much money did they share in total?
- Find the difference in ratio parts: 5 - 3 = 2 parts represents the 24 pound difference.
- Find the value of 1 part: 24 / 2 = 12 pounds.
- Find the younger brother's share: 3 parts x 12 = 36 pounds.
- Find the elder brother's share: 5 parts x 12 = 60 pounds.
- Add the two shares to find the total: 36 + 60 = 96 pounds.
- Final answer: they shared 96 pounds in total.
Practice questions
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Q1Share 40 sweets in the ratio 2:3. How many does each person get?Show answer
Answer: 16 and 24 (1 part = 40 / 5 = 8)
Q2Share 60 pounds in the ratio 1:2:3 among three people. How much does each get?Show answer
Answer: 10 pounds, 20 pounds and 30 pounds (1 part = 60 / 6 = 10)
Q3In a fruit bowl, the ratio of apples to oranges is 3:4. If there are 12 apples, how many oranges are there?Show answer
Answer: 16 (scale factor 12 / 3 = 4, so 4 x 4 = 16)
Q4A recipe requires flour and sugar in the ratio 5:2. If 250g of flour is used, how much sugar is needed?Show answer
Answer: 100g (scale factor 250 / 5 = 50, so 2 x 50 = 100)
Q5Two numbers are in the ratio 7:3 and differ by 20. What is the smaller number?Show answer
Answer: 15 (difference in parts is 7 - 3 = 4, so 1 part = 5, and 3 x 5 = 15)
Q6Express the ratio 2:5 as a fraction of the whole for each part.Show answer
Answer: 2/7 and 5/7
Exam-style questions
Written in the style of a 11+ exam paper, with a full mark scheme.
A charity shares a donation between two projects in the ratio 5:7. Project B receives 84 pounds more than Project A. How much did Project A receive?
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A fruit drink is made from apple, orange and mango juice in the ratio 3:2:1. A jug holds 900ml of the drink in total. How much mango juice does the jug contain, and what fraction of the jug is orange juice?
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Free printable worksheet
Want more practice on paper? Download the ratio and proportion depth 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 3 of 11+ Maths Workbook 2, the whole course as one free printable PDF.
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