Ratio Sharing when the Difference is Given
Ratio sharing when the difference is given covers sharing an amount between two or more people using a ratio, when the question states how much more one share is than another rather than stating the total. Pupils must first find the value of one 'part' of the ratio from that difference, which is a common trap on 11+ papers because the standard sharing method (dividing a known total by the number of parts) does not directly apply.
Method
- Write down the ratio and find how many parts separate the two shares by subtracting the smaller ratio number from the larger.
- Divide the given difference by this number of parts to find the value of one part.
- Multiply the value of one part by each number in the ratio to find every person's share.
- Add the shares together afterwards if the question also asks for the total amount.
- Check your answer by subtracting the two shares you found; the result should match the difference given in the question.
- In a three-part ratio, re-read the question carefully to see exactly which two shares the stated difference is between, since it may not be the two extreme values.
Worked example
Ravi and Sam share some sweets in the ratio 2 : 5. Sam receives 18 more sweets than Ravi. How many sweets does each person receive?
- Find the number of parts between them: 5 - 2 = 3 parts.
- Divide the difference by the number of parts to find the value of one part: 18 / 3 = 6.
- Find Ravi's share: 2 x 6 = 12.
- Find Sam's share: 5 x 6 = 30.
- Check: 30 - 12 = 18, which matches the difference given in the question.
Practice questions
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Q1Two amounts are in the ratio 3 : 4, and the larger amount is 15 more than the smaller. Find the value of one part of the ratio.Show answer
Answer: 15 (4 - 3 = 1 part, and 15 / 1 = 15)
Q2A and B share money in the ratio 2 : 7. B receives 30 pounds more than A. How much does A receive?Show answer
Answer: 12 pounds (7 - 2 = 5 parts, 30 / 5 = 6, and 2 x 6 = 12)
Q3Two numbers are in the ratio 5 : 8, and their difference is 21. Find the two numbers.Show answer
Answer: 35 and 56 (8 - 5 = 3 parts, 21 / 3 = 7, so the numbers are 5 x 7 = 35 and 8 x 7 = 56)
Q4Two shares are in the ratio 1 : 6, and the difference between them is 40. Find the total of the two shares.Show answer
Answer: 56 (6 - 1 = 5 parts, 40 / 5 = 8, so the shares are 8 and 48, giving a total of 56)
Q5Two jars of sweets are in the ratio 4 : 9. The larger jar has 25 more sweets than the smaller jar. How many sweets are in the smaller jar?Show answer
Answer: 20 (9 - 4 = 5 parts, 25 / 5 = 5, and 4 x 5 = 20)
Q6True or False: to solve a ratio problem given the difference between two shares, you divide the difference by the sum of the ratio parts.Show answer
Answer: False (you divide by the difference between the ratio parts, not their sum)
Q7Explain why you divide by the difference between the ratio numbers, rather than their sum, when you are given the difference between two shares.Show answer
Answer: The difference between the ratio numbers shows how many equal parts separate the two shares, so dividing the given difference by that number of parts finds the value of one part; dividing by the sum would instead be correct if you had been given the total of the shares, not the difference.
Exam-style questions
Written in the style of a 11+ exam paper, with a full mark scheme.
Two garden plots have areas in the ratio 3 : 7. The larger plot is 36 square metres bigger than the smaller plot. Work out the area of each plot.
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Three friends, Nia, Omar and Priya, share a sum of money in the ratio 2 : 3 : 5. Priya receives 45 pounds more than Nia. (a) Work out the value of one part of the ratio. (b) Work out how much each friend receives. (c) Work out the total amount of money shared.
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Free printable worksheet
Want more practice on paper? Download the ratio sharing when the difference is given 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 6 of 11+ Maths Workbook 2, the whole course as one free printable PDF.
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