Robinson Tuition
Year 9 · Key Stage 3 · free KS3 maths worksheet

Ratio and proportion

14 original questions, 36 marks. Type your answers below for an instant mark and a score (algebra in any equivalent form, e.g. 2sqrt(3) or 2√3), or print the worksheet, mark it with the answers sheet, and use the solutions to see every step written out by hand.

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The questions

1

Write down the ratio 42 : 6 in the form n : 1.

1 mark
Show answer
7 : 1
2
  1. Write the ratio 8 : 28 in the form 1 : n
  2. A school has 15 teachers and 360 pupils. Write the ratio of teachers to pupils in the form 1 : n
2 marks
Show answer
a) 1 : 3.5 b) 1 : 24
3

In a gym class, the ratio of the number of men to the number of women is 4 : 5.

There are 20 men in the class.

Work out the total number of people in the class.

2 marks
Show answer
45
4

Kofi makes two jugs of orange squash.

Jug A: 150 ml of squash mixed with 600 ml of water.
Jug B: 200 ml of squash mixed with 900 ml of water.

Which jug has the stronger taste of orange? Show your working by writing each ratio of squash to water in the form 1 : n

2 marks
Show answer
Jug A (1 : 4 compared with 1 : 4.5)
5

Amir, Bella and Carl share £132 in the ratio 1 : 4 : 6.

Work out how much money each of them gets.

3 marks
Show answer
Amir) £12 Bella) £48 Carl) £72
6

The exchange rate is £1 = €1.14.

Nadia changes £250 into euros.

Work out how many euros she gets.

2 marks
Show answer
€285
7

5 miles is about 8 kilometres.

  1. A school fun run is 12 km long. Work out about how many miles this is.
  2. A road sign says London is 25 miles away. Work out about how many kilometres this is.
2 marks
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a) 7.5 miles b) 40 km
8

3 kg of potatoes cost £2.64.

Work out the cost of 7 kg of these potatoes.

3 marks
Show answer
£6.16
9

Here are the prices of cinema tickets at two cinemas.

Number of tickets258
Cinema A cost£13£32.50£52
Cinema B cost£14£30£46
  1. At one cinema the cost is directly proportional to the number of tickets. Which cinema? Give a reason.
  2. Work out the cost of 11 tickets at that cinema.
3 marks
Show answer
a) Cinema A, because every ticket costs £6.50 b) £71.50
10

Each month Tom is paid £1800.

He saves 20% of the £1800.

He splits the rest between rent and bills in the ratio 5 : 3.

Work out how much Tom spends on rent each month.

3 marks
Show answer
£900
11

3 identical machines take 10 hours to print an order of leaflets.

Work out how long 5 of these machines would take to print the same order.

2 marks
Show answer
6 hours
12

In a fruit bowl there are apples, bananas and pears.

The ratio of apples to bananas is 3 : 2.

The ratio of bananas to pears is 4 : 3.

There are 24 apples in the bowl.

Work out the number of pears in the bowl.

3 marks
Show answer
12

Extension questions: beyond the core Year 9 objectives, for pupils who want a stretch.

13

y is directly proportional to x. When x = 6, y = 15

  1. Find a formula for y in terms of x.
  2. Work out the value of y when x = 10
  3. Work out the value of x when y = 40
3 marks
Show answer
a) y = 2.5x b) 25 c) 16
14

Leah and Sam share £480 in the ratio 5 : 7.

Sam gives 30% of his share to charity.

Leah gives £60 of her share to charity.

Sam gives more money to charity than Leah does.

Work out how much more.

5 marks
Show answer
£24

Your score

Answer the questions above and your score appears here.

Every question here is original and written by Robinson Tuition. It follows the Key Stage 3 programme of study; Year 9 sheets end with extension questions for top sets.

All Year 9 topics