Ratio, proportion and rates of change worksheet — GCSE Foundation

1.Write 250 g : 2 kg as a ratio in its simplest form.

2.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.

3.A market stall sells apples at a fixed price per kilogram. Priya buys 3 kg for £5.40. Write the ratio of the mass in kilograms to the cost in pounds, in its simplest form.

4.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.

5.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.

6.There are 400 students at a school. 25% of them have a brother, 40% have a sister and 15% have both a brother and a sister. Work out how many of the students have neither a brother nor a sister.

7.The length of ribbon A is 5/12 of the length of ribbon B. Write the length of ribbon B as a fraction of the length of ribbon A.

8.A printer prints at a constant rate. The time taken to print a batch of forms is inversely proportional to the printer's speed, in pages per minute. Printing at 20 pages per minute takes 15 minutes. Work out how long the same batch takes to print at 25 pages per minute. Give your answer in minutes.

9.A shade of paint is made by mixing blue paint and white paint. To make 5 litres of the shade, 2 litres of blue paint is used and the rest is white paint. Write the ratio of blue paint to white paint in its simplest form.

10.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.

11.Two numbers are in the ratio 5 : 8. The larger number is 40. Work out the smaller number.

12.Write the ratio 2/3 : 1/2 as a ratio of whole numbers, in its simplest form.

13.£2000 is invested in a savings account that pays 5% compound interest each year. Work out the value of the investment at the end of 2 years.

14.A cyclist rides 30 km in 1 hour 30 minutes. Work out the average speed of the cyclist in km/h.

15.A car travels 90 km using 6 litres of petrol. Work out how far the car can travel, at the same rate, using 9 litres of petrol.