Ratio, proportion and rates of change worksheet — GCSE Foundation

1.The number of pupils who walk to school is 3 times the number who cycle. Write the ratio of the number who cycle to the number who walk, in its simplest form.

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

3.Isla and her brother share £60 in the ratio 1:2. Work out Isla's share.

4.A recipe uses flour, sugar and butter in the ratio 8 : 3 : 5. Write the ratio of flour to the rest of the mixture (sugar and butter combined) in its simplest form.

5.A map's scale is given as '1 cm represents 2 km'. Write this scale in the form 1 : n.

6.£5000 is invested in an account paying 4% compound interest each year. Work out the total interest earned after 3 years.

7.Two mathematically similar circles have radii 4 cm and 20 cm. Write the ratio of the area of the smaller circle to the area of the larger circle in its simplest form.

8.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.

9.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.

10.A map has a scale of 1 : 25 000. A footpath measures 6 cm on the map. Work out the real length of the footpath, in kilometres.

11.y is always the same multiple of x. When x = 6, y = 15. Work out the value of y when x = 10.

12.Simplify the ratio 45 : 30 : 75 to its simplest form.

13.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.

14.A sum of £150 is divided between Ben and Chloe in the ratio 2:3. Work out Chloe's share.

15.After a 20% discount, a jacket costs £48. Work out the original price of the jacket.