Topics / Maths
Ratio and proportion
Ratio questions appear in almost every London grammar maths paper, and at Stage 2 they are usually hidden inside a multi-step word problem. The skill is always the same: turn the ratio into equal 'parts', find what one part is worth, then answer the question that was actually asked.
What is tested
- Sharing an amount in a given ratio (two or three parts)
- Finding a total or a difference from one known quantity
- Simplifying ratios and comparing them
- Ratio combined with fractions, percentages or changing quantities
Worked example
Red and blue counters are in the ratio 3 : 5. There are 40 counters altogether. How many are blue?
- Add the parts: 3 + 5 = 8 parts in total.
- One part = 40 ÷ 8 = 5 counters.
- Blue is 5 parts, so 5 × 5 = 25.
- Check: red = 3 × 5 = 15, and 15 + 25 = 40.
Answer: 25 blue counters
Exam-day checklist
- Write the ratio, then add the parts to get the total number of parts.
- Work out the value of ONE part before doing anything else.
- Re-read the question: are you asked for one share, the largest share, or the difference?
- Check that your shares add back up to the total.
Common mistakes
- Dividing the total by the ratio numbers (40 ÷ 5) instead of by the total number of parts.
- Giving the value of one part when the question asks for a share.
- When told 'there are 12 more girls than boys', treating 12 as the total rather than as the difference between parts.
Try it yourself
1. Share £72 in the ratio 2 : 3 : 4. What is the largest share?
Show answer
£32
2 + 3 + 4 = 9 parts; one part = 72 ÷ 9 = £8; the largest share is 4 × 8 = £32.
2. The ratio of boys to girls in a club is 4 : 5. There are 12 more girls than boys. How many children are in the club?
Show answer
108
The difference is 1 part = 12. There are 4 + 5 = 9 parts, so 9 × 12 = 108.
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