Ratio, proportion and rates of change worksheet — GCSE Foundation

1.A coach travels the 54 miles from London to Brighton in 1 hour 30 minutes. Work out the average speed of the coach, in mph.

2.A company's turnover was £128 000 in 2023 and £176 000 in 2024. Work out the multiplier that changes the 2023 turnover into the 2024 turnover.

3.A footpath is drawn 3 cm long on a map with a scale of 1 : 50 000. Work out the real length of the footpath, in metres.

4.A watering can holds 4500 cm³ of water. Given that 1 litre = 1000 cm³, work out the capacity of the watering can in litres.

5.A tap fills a tank at a rate of 15 litres per minute. Given that 1 litre = 1000 cm³, work out the rate at which the tank fills in cm³ per second.

6.A parcel has a mass of 2400 g. Given that 1 kg = 1000 g, work out the mass of the parcel in kilograms.

7.A car is bought for £9000. Its value decreases by 8% each year. Work out its value after 2 years.

8.The mass of a length of copper pipe is proportional to its length. A pipe of length 4.5 m has a mass of 12.6 kg. Work out the mass of a pipe of the same type of length 9.5 m.

9.Triangle A and triangle B are mathematically similar. A side of triangle A is 5 cm long, and the corresponding side of triangle B is 15 cm long. Write the ratio of the length in triangle A to the length in triangle B in its simplest form.

10.y is directly proportional to x. When x = 7, the value of y is 21. Work out the value of x when y = 12.

11.To make a shade of green paint, the amount of yellow paint used is always 0.75 times the amount of blue paint used. Write the amount of blue paint as a fraction of the amount of yellow paint, in its simplest form.

12.The same jumper is sold at two shops. Shop A charges £40 and Shop B charges £50. Write down the price at Shop A as a percentage of the price at Shop B.

13.In a school choir the ratio of boys to girls is 3:4. When 6 more boys join the choir, the ratio of boys to girls becomes 1:1. Work out how many girls are in the choir.

14.A film runs for 2.25 hours. Work out the length of the film in minutes.

15.A garden centre has 90 rose bushes in stock. It receives a delivery that increases its stock of rose bushes by 20%. In the same week it sells 150 lavender bushes. Work out the new number of rose bushes, then write it as a fraction of the number of lavender bushes sold, giving your answer in its simplest form.