Ratio, proportion and rates of change worksheet — GCSE Foundation

1.Simplify the ratio 12 : 18 : 30 to its simplest form.

2.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.

3.A map has a scale of 1 : 50 000. Two villages are 4 cm apart on the map. Work out the real distance between the villages, in kilometres.

4.Write £3.60 : £2.40 as a ratio in its simplest form.

5.The rent on a flat increases by 10% one year and by a further 10% the following year. Work out the overall percentage increase over the two years.

6.A sunflower is 140 cm tall. A tomato plant is 80 cm tall. Write the height of the tomato plant as a fraction of the height of the sunflower, giving your answer in its simplest form.

7.A metal block has a mass of 270 g and a volume of 30 cm³. Work out the density of the block, in g/cm³.

8.A recipe requires flour and butter in the ratio 3 : 2. Write down which of these amounts could be used in the recipe.

9.A fruit bowl contains 9 apples and 21 oranges. Write down the ratio of apples to oranges in its simplest form.

10.A toy manufacturer makes a model aircraft that is mathematically similar to the real aircraft, at a scale of 1 : 48. The wingspan of the model is 15 cm. Work out the wingspan of the real aircraft, giving your answer in metres.

11.Rice costs £3.20 per kg. Work out the cost of the rice in pence per 100 g.

12.A bag contains 7 red counters and 15 blue counters. Write down the ratio of red counters to blue counters in its simplest form.

13.x is 2/3 of y. Write the ratio x : y in its simplest form.

14.A straight-line graph passes through the origin and the point (4, 10). The line represents y = kx. Write down the ratio x : y in its simplest form.

15.Which of these ratios is equivalent to 6 : 10 : 14?