Ratio, proportion and rates of change worksheet — GCSE Foundation

1.A prize fund of £240 is shared between two winners in the ratio 3 : 5. Write the smaller winner's share as a fraction of the whole prize fund.

2.40% of a number is 12 more than 25% of the same number. Work out the number.

3.A vegetable patch is divided between carrots, potatoes and onions in the ratio 2 : 3 : 5. Write down the fraction of the patch used for potatoes.

4.y is inversely proportional to x. When x = 5, y = 8. Work out the value of y when x = 10.

5.A parcel has a mass of 2400 g. Given that 1 kg = 1000 g, work out the mass of the parcel in kilograms.

6.A tank is filled at a rate of 3 litres every 2 minutes. Given that 1 litre = 1000 cm³, work out the flow rate in cm³ per minute.

7.Two mathematically similar hexagonal tiles have areas 18 cm² and 50 cm². Work out the ratio of the side length of the smaller tile to the side length of the larger tile, in simplest form.

8.A journey to school takes 12 minutes. A journey to the gym takes 20 minutes. Write the time for the journey to school as a fraction of the time for the journey to the gym, giving your answer in its simplest form.

9.A rectangular garden has its length and width in the ratio 5:3. Given that the perimeter of the garden is 64 m, work out the width of the garden.

10.The mass of a length of copper pipe is proportional to its length. A pipe of length 4.5 m has a mass of 12.6 kg. Work out the mass of a pipe of the same type of length 9.5 m.

11.An oven is preheating. Its temperature, T °C, is plotted against time, t minutes, on a straight-line graph. The line passes through the points (2, 60) and (6, 140). Work out the gradient of the line.

12.Two mathematically similar rectangles have widths 5 cm and 10 cm. The perimeter of the smaller rectangle is 18 cm. Work out the perimeter of the larger rectangle.

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

15.A printer prints pages at a constant rate. It prints 45 pages in 6 minutes. Work out how many pages it prints in 10 minutes.