MathsIntermediateGCSE (Years 10–11) · Ages 14–16

GCSE Maths: Ratio and Proportion

A GCSE maths ratio and proportion worksheet covering simplifying ratios, dividing quantities in a given ratio, direct and inverse proportion, and proportion word problems.

Generate your own

Learning objectives

Simplify ratios and express them in the form 1:n
Divide a quantity into a given ratio
Solve problems involving direct and inverse proportion

Instructions

Show all working. Where appropriate, give answers to 2 decimal places unless the question asks otherwise.

Questions

Simplify the ratio 24:36.

Write the ratio 15:25 in the form 1:n.

Divide £120 in the ratio 3:5.

Share 84 in the ratio 1:2:4.

A recipe for 4 people needs 320 g of flour. How much flour is needed for 7 people?

If y is directly proportional to x, and y = 18 when x = 6, find y when x = 10.

If y is inversely proportional to x, and y = 8 when x = 3, find y when x = 6.

In a bag of sweets, the ratio of red to green to yellow is 3:4:5. There are 36 sweets in total. How many of each colour are there?

A car travels 180 miles on 12 litres of fuel. How far will it travel on 20 litres?

5 workers can build a wall in 12 days. How many days would it take 3 workers to build the same wall? (Assume all workers work at the same rate.)

Map scale: 1 cm represents 5 km. Two cities are 8.4 cm apart on the map. What is the real distance?

The ratio of boys to girls in a school is 7:9. If there are 432 pupils in total, how many are boys?

Answer Key

Teacher / Parent copy

1.2:3

2.1:5/3 or 1:1.67 (15:25 → divide both by 15 → 1:25/15 = 1:5/3)

3.£45 and £75 (total parts = 8; each part = £15; 3 × 15 = £45, 5 × 15 = £75)

4.12, 24, and 48 (total parts = 7; each part = 12)

5.560 g (320 ÷ 4 = 80 g per person; 80 × 7 = 560 g)

6.y = 30 (k = 18/6 = 3; y = 3 × 10 = 30)

7.y = 4 (k = 8 × 3 = 24; y = 24 ÷ 6 = 4)

8.Red: 9, Green: 12, Yellow: 15 (total parts = 12; each part = 3)

9.300 miles (180 ÷ 12 = 15 miles per litre; 15 × 20 = 300)

10.20 days (inverse proportion: 5 × 12 = 60; 60 ÷ 3 = 20)

11.42 km (8.4 × 5 = 42)

12.189 boys (total parts = 16; each part = 27; 7 × 27 = 189)

Teacher note

Ratio and proportion is consistently one of the highest-weighted topics on GCSE Maths papers. Questions 6 and 7 introduce proportionality constants, which students often find abstract — emphasise the two-step method (find k, then use k). Question 10 is a classic inverse proportion trap question.

Generate a custom Maths worksheet

This sample covers Ratio and Proportion. Our AI can generate a fresh worksheet on any topic, any age group, in seconds — including answer keys.

Generate Free Worksheet

7-day free trial · No card required

More free worksheets

Maths · Year 2