Ratio questions with full solutions for Pearson Edexcel International GCSE Mathematics A (4MA1), Higher tier. Read the 3 worked examples first, then cover each solution and redo it yourself.
Ratio & proportion: Sharing quantities in a given ratio and solving direct proportion problems.
Ratio 1: Sharing quantities in a ratio.
Ratio 2: Direct and inverse ratio problems.
Ratio worked examples
Worked example 1: Sharing in a ratio
Share £72 in the ratio 5 : 3.
Solution
Total parts: \(5+3=8\).
One part: \(72\div8=9\).
Shares: \(5\times9=45\) and \(3\times9=27\).
Check: \(45+27=72\).
Answer: £45 and £27
Tip: Always check the shares add back to the total.
Worked example 2: Simplifying a three-part ratio
Write 45 : 60 : 75 in its simplest form.
Solution
The HCF of 45, 60 and 75 is 15.
Divide each part by 15: 3 : 4 : 5.
Answer: 3 : 4 : 5
Tip: Divide by the HCF in one step.
Worked example 3: Ratio from a difference
The ratio of A's money to B's money is 4 : 7. B has £36 more than A. How much does each have?
Solution
The difference is \(7-4=3\) parts.
3 parts = £36, so 1 part = £12.
A: \(4\times12=48\); B: \(7\times12=84\).
Answer: A £48, B £84
Tip: Match the given amount to the correct number of parts.
Every question and worked example here is original, written for IGCSE Math Revision rather than copied from Pearson papers, and each answer was re-solved independently before publishing.
Either Higher tier paper, 1H or 2H, can test ratio: both cover the whole Pearson Edexcel International GCSE Mathematics A (4MA1) specification and both allow a calculator. Show your method, because most marks are for working.
Where can I practise more ratio questions?
In the IGCSE student hub: Unit 1 (Number) has more exam-style questions on this topic, each with a mark scheme. Practice starts with a 7-day free trial; the worked examples and questions on this page are free.
IGCSE Math Revision