GCSE Maths → Ratio → Ratio Word Problems
Ratio Word Problems GCSE Maths
Ratio word problems are common in GCSE maths. They often appear in questions about sharing money, recipes, sweets, mixtures, maps, groups of people, and real-life comparisons.
Many students find ratio difficult not because the calculations are always hard, but because the question is written in words. The key is to identify whether you are given the total amount or one known share.
Video explanation
A short Worthing Maths Tutor video explanation for ratio word problems GCSE maths can be embedded here later to improve student engagement and time on page.
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.
total parts = 2 + 3 = 5
Method 1: sharing a total amount in a ratio
- Add the ratio parts.
- Divide the total amount by the total number of parts.
- Multiply by each ratio part.
- Check that the shares add back to the original total.
Example 1: Share £60 in the ratio 2:3
Ali and Ben share £60 in the ratio 2:3.
Add the ratio parts:
Find one part:
Find each share:
Check:
Example 2: Share 80 sweets in the ratio 3:5
Add the ratio parts:
Find one part:
Find each share:
Method 2: when one share is already known
Sometimes the question gives one person’s share instead of the total. In that case, use the known share to find one part.
Example 3: One amount is known
Tom and Jack share money in the ratio 3:5. Tom gets £24. How much does Jack get?
Tom has 3 parts, and 3 parts = £24.
Jack has 5 parts.
Jack gets £40.
Example 4: Finding the total from one share
A and B share money in the ratio 4:7. B gets £35. Find the total amount.
B has 7 parts, and 7 parts = £35.
Total parts:
Total amount:
Recipe ratio problems
Recipe questions often use the same ratio method. First find one part, then scale the quantities up or down.
Example 5: Flour and sugar ratio
Flour and sugar are mixed in the ratio 4:1. There are 500 g of mixture in total. How much flour is there?
Total parts:
One part:
Flour is 4 parts:
How to choose the correct method
- If the total is given, add the ratio parts and divide the total.
- If one share is given, use that share to find one part.
- If the question asks for the total, add all parts after finding one part.
- If the question asks for the difference, find both shares first.
Common mistakes in ratio word problems
- Forgetting to add the ratio parts first.
- Dividing by one ratio part instead of total parts.
- Mixing up which person gets which share.
- Assuming the given number is always the total.
- Not checking whether the shares add back correctly.
- Stopping too early before answering the actual question.
Practice questions
- Share £42 in the ratio 1:2.
- Share 80 sweets in the ratio 3:5.
- Red to blue counters are in the ratio 2:7. There are 63 counters in total. How many are red?
- Anna and Sam share money in the ratio 4:3. Anna gets £28. How much does Sam get?
- A and B share money in the ratio 5:2. B gets £18. Find the total amount.
- Flour and sugar are mixed in the ratio 5:2. There are 700 g of mixture. How much sugar is there?
Answers
- £14 and £28
- 30 sweets and 50 sweets
- 14 red counters
- £21
- £63
- 200 g
Ratio word problems FAQ
What is a ratio word problem?
A ratio word problem is a question where quantities are compared or shared using a ratio, often in contexts such as money, sweets, recipes, mixtures, or groups.
How do you solve sharing in a ratio questions?
Add the ratio parts, divide the total by the total number of parts, then multiply by each ratio part.
Why do students struggle with ratio word problems?
Students often struggle because they divide by the wrong number, mix up the ratio parts, or do not identify whether the total amount or one share is given.
Are ratio word problems on GCSE maths?
Yes. Ratio word problems are common on GCSE maths papers and appear in both Foundation and Higher tier questions.
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