Ratio, proportion and rates of change worksheet — GCSE Foundation

1.Two numbers are in the ratio 2 : 3. The smaller number is 8. Work out the larger number.

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 cyclist travels 18 km in 45 minutes. Work out the average speed, in km/h.

4.Write the ratio 2 : 1/4 as a ratio of whole numbers in its simplest form.

5.A map has a scale of 1 : 100. A path measures 5 cm on the map. Work out the real length of the path, in metres.

6.A straight-line graph shows the cost, C pounds, of hiring a small van for m miles driven. The line passes through the origin and the point (25, 20). Work out the gradient of the line.

7.6 identical printers can print a batch of exam papers in 40 minutes, all working at the same rate. Working at the same rate, work out how many minutes 4 of these printers would take to print the same batch.

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

9.Maya buys a vintage car for £15000. Its value is expected to increase by 4% each year for 2 years. She then plans to sell the car and use £2000 of the money from the sale to buy a trailer. Work out how much money she will have left after selling the car and buying the trailer.

10.A 5 kg bag of potatoes costs £4.50. Work out the cost per kilogram.

11.A material has a density of 2 g/cm³. Work out the mass of 5 cm³ of this material.

12.Write 1/5 as a percentage.

13.A coach journey is 372 miles in total. After a stop, the coach has travelled 217 miles. Write the distance still to travel as a fraction of the total journey. Give your answer in its simplest form.

14.A car is bought for £17,500. Its value decreases by 12% in the first year, and by a further 10% of its reduced value in the second year. Work out the value of the car at the end of the second year, giving your answer to the nearest pound.

15.A map has a scale of 1 : 40 000. A cycle path measures 7.5 cm on the map. Work out the real length of the cycle path, in kilometres.