Ratio, proportion and rates of change worksheet — GCSE Foundation

1.A map has a scale of 1 : 1000. A road is 300 m long in real life. Work out the length of the road on the map, in centimetres.

2.Two numbers are in the ratio 3 : 7. Their sum is 60. Work out the positive difference between the two numbers.

3.A recipe for 6 muffins needs 150 g of flour. Aisha wants to make 15 muffins using the same recipe. Work out how much flour she needs.

4.Order these three values from smallest to largest: 3/8, 0.43, 41%.

5.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.

6.In a fruit bowl, the ratio of apples to oranges is 5 : 3. Work out what percentage of the fruit in the bowl is apples.

7.A printer prints pages at a constant rate. It prints 45 pages in 6 minutes. Work out how many pages it prints in 10 minutes.

8.Two mathematically similar oil drums have a length scale factor of 3 from the smaller drum to the larger drum. Work out the volume scale factor from the smaller drum to the larger drum.

9.In a science lesson Priya has 10 litres of a solution that is 30% salt. She adds water to make a solution that is 20% salt. Work out how many litres of water she adds.

10.A water butt is being filled from a hosepipe at a constant rate while a small leak drains water out at a constant rate, giving a constant net rate of change. The volume of water in the butt, V litres, is shown on a straight-line graph against time, t minutes. The line passes through the points (5, 20) and (15, 60). The butt is empty at t = 0. Work out how many minutes it takes to reach a volume of 100 litres.

11.Three friends share a raffle prize of £360 in the ratio 2:3:4. Work out the share of the friend whose part of the ratio is 3.

12.Jamal is paid £54 for working 6 hours. Work out his rate of pay, in £ per hour.

13.Map A has a scale of 1 : 25000 and Map B has a scale of 1 : 50000, both showing the same area. A real distance of 10 km is measured on each map. On which map does this distance appear as the longer length, and how long is it on that map, in centimetres?

14.The ratio of cats to dogs in a shelter is 3:4. There are 18 cats. Work out the total number of animals in the shelter.

15.Two quantities x and y are inversely proportional. When x = 2, the value of y is 15. Work out the value of y when x = 5.