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Ratio Word Problems GCSE Maths

Ratio word problems are very common in GCSE Maths. They often appear in questions about sharing amounts, recipes, money, mixtures, and groups of people.

The key idea is to split a total amount into parts according to a given ratio.

What Is a Ratio?

A ratio compares parts.

For example, if red sweets and blue sweets are in the ratio 2:3, that means:

  • for every 2 red sweets
  • there are 3 blue sweets

How to Solve Ratio Sharing Problems

Example:

£60 is shared between Ali and Ben in the ratio 2:3. How much does each get?

Step 1: Add the parts of the ratio

2 + 3 = 5

Step 2: Divide the total by 5 to find one part

60 ÷ 5 = 12

Step 3: Multiply by the ratio parts

Ali gets: 2 × 12 = £24

Ben gets: 3 × 12 = £36

Example with a Recipe

Flour and sugar are mixed in the ratio 4:1. If there are 500g of mixture in total, how much flour is there?

Step 1: Add the parts

4 + 1 = 5

Step 2: Divide total by 5

500 ÷ 5 = 100

Step 3: Multiply by the flour part

4 × 100 = 400g

Example Where One Amount Is Known

Tom and Jack share money in the ratio 3:5. Tom gets £24. How much does Jack get?

If 3 parts = £24, then 1 part = £8.

Jack gets 5 parts:

5 × £8 = £40

Common Mistakes

  • forgetting to add the ratio parts first
  • dividing by one of the parts instead of the total number of parts
  • mixing up which person or quantity gets which share
  • not checking whether the answer adds back to the original total

Quick Practice Questions

  1. Share £42 in the ratio 1:2.
  2. Share 80 sweets in the ratio 3:5.
  3. Red to blue counters are in the ratio 2:7. There are 63 counters in total. How many are red?
  4. Anna and Sam share money in the ratio 4:3. Anna gets £28. How much does Sam get?

Answers

  1. £14 and £28
  2. 30 and 50
  3. 14
  4. £21

Final Tip

In ratio word problems, first decide whether you are finding one part from the total, or one part from a known share. That usually makes the method much clearer.