Ratio, proportion and rates of change worksheet — GCSE Foundation

1.A company had 8000 employees. The number of employees decreased by 5% in the first year, and then increased by 5% in the second year. Work out the number of employees at the end of the second year, to the nearest whole number.

2.y is directly proportional to x, and y = 7x. Work out the value of x when y = 35.

3.A box contains 12 red counters and 18 blue counters. Write the number of red counters as a fraction of the number of blue counters. Give your answer in its simplest form.

4.A room plan is drawn to a scale of 1 : 50. A wall in the room is 4 m long in real life. Work out the length of the wall on the plan, in centimetres.

5.y is directly proportional to x. When x = 2, y = 9. Which of these pairs of values is also consistent with this proportion?

6.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.

7.Two printers' running costs are shown on separate straight-line graphs of total cost against number of pages printed. Printer A's graph has gradient £0.04 per page. Printer B's graph has gradient £0.05 per page. Work out how much cheaper it is to print 200 pages on Printer A than on Printer B, based on these running costs alone.

8.A cyclist travels 45 km in 3 hours at a constant speed. Work out the cyclist's average speed, in km/h.

9.y is directly proportional to x. If the value of x is trebled (multiplied by 3), what happens to the value of y?

10.£96 is shared between Ben, Cara and Dev in the ratio 2:3:7. Work out how much Cara receives.

11.Write the ratio 8 : 15 in the form 1 : n.

12.A runner's speed is 8 m/s. Given that there are 3600 seconds in an hour and 1000 metres in a kilometre, work out the runner's speed in km/h.

13.An adult cinema ticket costs £15 and a child ticket costs £9. Write the ratio of the adult price to the child price in its simplest form.

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

15.Isla says that the ratio 4:6 is equivalent to the ratio 6:9. Is she correct? Give a reason for your answer.