Share an amount in a given ratio, and work backwards when you know one share or the difference between shares. It is on Foundation and Higher, aimed at grade 3. Free questions with answers are on this page. Worked examples show each line before you try the questions.
Sharing in a ratio is splitting a total into equal parts, then giving each person their number of parts. 2:3 with a total of £80 is 5 parts of £16, so £32 and £48. Check by adding: the shares must return the original total.
Sometimes the total is not given — one person's share is. Then one part is that share divided by their number of parts, and everyone else scales from there. 'A has £12 more than B' is a difference-of-parts question: the extra £12 equals the extra parts.
Add the parts, divide the total by that sum to find one part, multiply by each share. If you are given a difference or one share instead of the total, that difference is the gap between the parts.
Objectives
Add the ratio numbers. That is how many equal parts the whole makes.
Multiply one part by each number in the ratio.
The shares add back to the original amount.
Key points
Share a total amount in a two- or three-part ratio.
Find the total when you are told the value of one share.
Find the total when you are told the difference between two shares.
Check your shares add back up to the total.
Worked examples
Example 1
Share £15 in the ratio 2:3.
2 marks
The ratio has 2 + 3 = 5 parts.
One part is £15 ÷ 5 = £3.
The shares are 2 × 3 = 6 and 3 × 3 = 9.
Answer: £6 and £9
Common slips
Slip: The ratio has 2 × 3 = 6 parts. The parts are added together, not multiplied.
Slip: One part is £15 ÷ 2 = £7.5. The total is divided by all the parts, not by the first ratio number.
Slip: Each person gets £3. The shares follow the ratio. Multiply one part by each ratio number.
Example 2
Share £20 in the ratio 1:4.
2 marks
The ratio has 1 + 4 = 5 parts.
One part is £20 ÷ 5 = £4.
The shares are 1 × 4 = 4 and 4 × 4 = 16.
Answer: £4 and £16
Common slips
Slip: The ratio has 1 × 4 = 4 parts. The parts are added together, not multiplied.
Slip: One part is £20 ÷ 1 = £20. The total is divided by all the parts, not by the first ratio number.
Slip: Each person gets £4. The shares follow the ratio. Multiply one part by each ratio number.
Example 3
Share £40 in the ratio 3:5.
2 marks
The ratio has 3 + 5 = 8 parts.
One part is £40 ÷ 8 = £5.
The shares are 3 × 5 = 15 and 5 × 5 = 25.
Answer: £15 and £25
Common slips
Slip: The ratio has 3 × 5 = 15 parts. The parts are added together, not multiplied.
Slip: One part is £40 ÷ 3 = £13.33. The total is divided by all the parts, not by the first ratio number.
Slip: Each person gets £5. The shares follow the ratio. Multiply one part by each ratio number.
Questions and answers
GCSE Maths ratio questions and answers. Try each one, then open the answer. Easy questions come first.
Question 1 Easy2 marks
Share £32 in the ratio 3:5.
Show answer
Answer: 12, 20
There are 8 parts in £32.
One part is £4.
M1 — There are 8 parts in £32.
A1 — Answer 12, 20
Question 2 Easy2 marks
Share £24 in the ratio 1:2:3.
Show answer
Answer: 4, 8, 12
There are 6 parts in £24.
One part is £4.
M1 — There are 6 parts in £24.
A1 — Answer 4, 8, 12
Question 3 Medium2 marks
An amount is shared in the ratio 2:3. The larger share is £15. Give the total, the smaller share, then the larger share.
Show answer
Answer: 25, 10, 15
3 parts make £15.
One part is £5.
M1 — 3 parts make £15.
A1 — Answer 25, 10, 15
Question 4 Medium2 marks
Red and blue are in the ratio 2:3. Blue has 6 more than red. How many red counters are there?
Show answer
Answer: 12
The gap is 1 part, so one part is 6.
Red is 2 parts.
M1 — The gap is 1 part, so one part is 6.
A1 — Answer 12
Question 5 Hard2 marks
The ratio is 2:5, so the shares differ by 3 parts. The difference is £12. What is the total amount?
Show answer
Answer: 28
3 parts are £12.
7 parts are £28.
M1 — 3 parts are £12.
A1 — Answer 28
Question 6 Hard2 marks
Amy:Ben = 1:2 and Ben:Caz = 2:3. Together they share £60. Give Amy's, Ben's and Caz's shares in that order.
Show answer
Answer: 10, 20, 30
The linked ratio is 1:2:3.
There are 6 parts in £60.
M1 — The linked ratio is 1:2:3.
A1 — Answer 10, 20, 30
Question 7 Exam-style3 marks
The ratio is 2:5, so the shares differ by 3 parts. The difference is £15. What is the total amount?
Show answer
Answer: 35
3 parts are £15.
7 parts are £35.
M1 — 3 parts are £15.
M1 — 7 parts are £35.
A1 — Answer 35
Common mistakes
Most lost marks on this topic are one slip.
Dividing by one of the ratio numbers instead of the total parts.
Add the parts first.
Giving both people the same share.
The shares follow the ratio, unless the ratio is 1:1.
Checking by multiplying the shares.
Add the shares. They should return the total.
Spot the slip
The number of parts in 2:3 is
5
6
2
Show the slip
5 Add the parts to see how many equal shares the whole is split into.
Exam tips
This topic can appear on a calculator or a non-calculator paper. Show enough working for a method mark.
If the question says “show that”, the result is given. The marks are for the steps that reach it.
The method is the same on AQA-style and Edexcel-style papers.
Write 'one part = …' as a line on its own — it is the key method mark.
Label your final shares with names or units (£80 and £100), not just numbers.
Printable worksheet
The same questions are in a PDF you can print. Answers start on a later page.