Ratio, proportion and rates of change worksheet — GCSE Foundation

1.Simplify the ratio 45 : 30 : 75 to its simplest form.

2.x × y is used to test whether two quantities are in inverse proportion. For the pairs x = 4, y = 15 and x = 6, y = 10, which statement is correct?

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.A conversion graph between kilometres and miles passes through the origin and the point (50, 31), with the number of kilometres on the horizontal axis and the number of miles on the vertical axis. Work out the number of miles equivalent to 1 kilometre.

5.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.

6.A shop buys a bike for £150 and sells it, making a profit of £45. Write the selling price as a fraction of the cost price, giving your answer in its simplest form.

7.In a choir of 30 singers, 40% are altos and the rest are sopranos. Write the number of sopranos as a fraction of the number of altos. Give your answer in its simplest form.

8.y is directly proportional to x. When x = 2, y = 9. Which of these pairs of values is also consistent with this proportion?

9.In a science lesson Priya has 10 litres of a solution that is 30% salt. She adds water to make a solution that is 20% salt. Work out how many litres of water she adds.

10.Write 3 hours 45 minutes as a decimal number of hours.

11.3 builders put up a fence in 12 days. All the builders work at the same rate, so the number of days is inversely proportional to the number of builders. Work out how long 9 builders take to put up the same fence.

12.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.

13.A jug holds 2 litres. Given that 1 litre = 1000 cm³, work out the capacity of the jug in cm³.

14.Write the ratio 6a : 9a in its simplest form, where a is a positive number.

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