Ratio, proportion and rates of change worksheet — GCSE Foundation

1.Water flows into a tank at a constant rate. After 8 minutes the tank holds 200 litres. Write the ratio of time in minutes to volume in litres, in its simplest form.

2.A plumber's charge, C pounds, for a job lasting h hours is shown on a straight-line graph. The line passes through the points (1, 45) and (3, 85). Work out what the gradient of this line represents, in context.

3.Write 400 g : 1.5 kg as a ratio in its simplest form.

4.The ratio of the number of red beads to blue beads in a bracelet is 3 : 7. There are 21 blue beads. Work out the number of red beads.

5.The price of a share falls by 10% on Monday and then rises by 10% on Tuesday. Work out the overall percentage change from Monday's starting price.

6.Triangle ABC has a right angle at C. AC = 3 cm and BC = 4 cm. Triangle ABC is mathematically similar to triangle PQR, with angle B corresponding to angle Q. Work out the value of tan(angle Q).

7.A cookery class lasts 45 minutes. A double lesson at school lasts 2 hours. Write the length of the cookery class as a fraction of the length of the double lesson. Give your answer in its simplest form.

8.A jumper costs £45 at Shop A, where it is reduced by 20%. The same jumper costs £34 at Shop B, where a further 10% reduction is then applied. Work out the difference between the two reduced prices.

9.Divide 84 in the ratio 3:4. Work out the smaller share.

10.£1 is worth 1.25 US dollars. Write the ratio of pounds to dollars in its simplest form, using whole numbers.

11.y is inversely proportional to x, and y = 20 ÷ x. Work out the value of y when x = 4.

12.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.

13.Zara is paid £9 per hour. Her wage is directly proportional to the number of hours she works. Work out her wage for working 6 hours.

14.Write 75p : £1.50 as a ratio of whole numbers in its simplest form.

15.In a class, 50% of the students study French, 30% study Spanish and the rest study German. Write down the ratio of French : Spanish : German students, in its simplest form.