Ratio, proportion and rates of change worksheet — GCSE Foundation

1.A journey takes 4 hours at an average speed of 60 km/h. The time taken is inversely proportional to the average speed. Work out how long the same journey takes at an average speed of 80 km/h.

2.A delivery driver travels 45 km in the first 30 minutes of a journey, and then a further 75 km in the next 1 hour. Work out her average speed for the whole journey, in km/h.

3.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.

4.Ravi has 5 pears. He has 4 times as many apples as pears. Write the number of pears as a fraction of the number of apples.

5.A bottle contains 1.5 litres of juice. Given that 1 litre = 1000 ml, work out the capacity of the bottle in millilitres.

6.The number of tickets a group can afford is inversely proportional to the price per ticket. At £4 per ticket, the group can afford 12 tickets. Work out how many tickets the group can afford at £6 per ticket.

7.Isla says that the ratio 4:6 is equivalent to the ratio 6:9. Is she correct? Give a reason for your answer.

8.y is always the same multiple of x. When x = 6, y = 15. Work out the value of y when x = 10.

9.Simplify the ratio 12 : 18 : 30 to its simplest form.

10.A table shows three pairs of values: when x = 2, y = 6; when x = 5, y = 15; when x = 8, y = 24. In every pair the ratio y : x is the same. Write down a formula for y in terms of x.

11.A concert hall has 54 seats in total, of which 24 are reserved and the rest are free. Write the number of free seats as a fraction of the number of reserved seats. Give your answer in its simplest form.

12.A scale drawing states '1 cm represents 25 m'. Which of these is the correct way to write this scale in the form 1 : n?

13.Priya is paid £58.50 for working 7.5 hours on a Saturday. Work out her rate of pay, in £ per hour.

14.In a bag, the ratio of green counters to yellow counters is 3 : 8. There are 24 yellow counters. A student says, 'There must be 9 green counters.' Is the student correct? Choose the correct verdict and reason.

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.