Example 1 · level 1 — a gentle start
Finn mixes 21 litres of paint in the ratio 1:2. How many litres is the larger part?
- 7
- 14
- 21
- 10.5
Answer: 14 — 1+2 = 3 parts, so one part is 21 ÷ 3 = 7. The larger share is 2 × 7 = 14.
11+ ratio and proportion questions
Ratio and proportion comes up in the maths paper of every major 11+ format. Here is what the questions look like, the method that works under time pressure, and five worked examples with the full reasoning, from a gentle start to a hard paper.
Maths · examined by GL and CEM · 5 worked examples
What your child needs to know
- A ratio shares things into parts. 1:2 means one part, then two.
- Add the parts to see how many altogether: 1 + 2 = 3 parts.
Where marks get lost: Divide the total by the parts, then multiply by the share you want.
Worked examples
Every question below is generated by the same engine your child practises on, and every answer is derived by our checker rather than written by hand — which is why we can put them on a public page at all.
Example 2 · level 2 — typical of early practice
Aisha mixes 64 litres of paint in the ratio 1:3. How many litres is the smaller part?
- 32
- 17
- 48
- 16
Answer: 16 — 1+3 = 4 parts, so one part is 64 ÷ 4 = 16. The smaller share is 1 × 16 = 16.
Example 3 · level 3 — standard paper difficulty
Share 125 in the ratio 2:3. What is the smaller share?
- 62.5
- 75
- 25
- 50
Answer: 50 — 2+3 = 5 parts, so one part is 125 ÷ 5 = 25. The smaller share is 2 × 25 = 50.
Example 4 · level 4 — a harder paper
Chloe and a friend share 273 sweets in the ratio 3:4. How many does the one with more get?
- 136.5
- 117
- 156
- 39
Answer: 156 — 3+4 = 7 parts, so one part is 273 ÷ 7 = 39. The larger share is 4 × 39 = 156.
Example 5 · level 5 — the level that separates candidates
Hari and a friend share 216 sweets in the ratio 5:7. How many does the one with fewer get?
- 18
- 108
- 126
- 90
Answer: 90 — 5+7 = 12 parts, so one part is 216 ÷ 12 = 18. The smaller share is 5 × 18 = 90.
How to practise this at home
- Work in short, frequent sessions. Ten minutes daily beats an hour at the weekend, because the recall gap is what builds memory.
- Insist on written working, even for questions your child can do in their head — under exam pressure the method is what survives.
- When an answer is wrong, ask them to explain their reasoning before you correct it. The error is almost always in one step, not the whole approach.
Practise ratio and proportion with a tutor that explains
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