Ratio, proportion and rates of change worksheet — GCSE Foundation

1.The number of biscuits, b, that each guest at a party receives is inversely proportional to the number of guests, g. Which equation could show this relationship?

2.A ratio is 3 : 5. Write the first part of the ratio as a fraction of the whole.

3.Write the ratio 18:22 in its simplest form.

4.A shop sells fruit juice concentrate that must be diluted with water in the ratio 2 : 5 (concentrate : water) to make squash. Priya has 8 litres of concentrate. Work out how much water she needs to keep the same ratio.

5.Two scale plans of the same football pitch are drawn: Plan A has a scale of 1 : 1000 and Plan B has a scale of 1 : 200. A pitch length is 8 cm on Plan A. Work out the length of the same pitch on Plan B, in centimetres.

6.The ratio of the amount Noah has saved to the amount Grace has saved is 4:5. Noah has saved £200. Work out how much they have saved altogether.

7.Write the ratio 4x : 6x in its simplest form, where x is a positive number.

8.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.

9.A block of wood has a mass of 60 g and a volume of 100 cm³. Work out the density of the block, in g/cm³.

10.A science technician mixes 400 g of a salt solution of concentration 5% with 100 g of a salt solution of concentration 25%. Work out the concentration of the mixture.

11.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.

12.For the pairs x = 6, y = 15 and x = 10, y = 25, which statement is correct?

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

14.Work out how many seconds there are in 3 minutes and 20 seconds.

15.An acid solution has a concentration of 20%. The solution contains 40 g of acid, and the rest of the solution is water. Work out the mass of water in the solution.