Ratio, proportion and rates of change worksheet — GCSE Foundation

1.Work out the time taken to travel 120 km at an average speed of 60 km/h.

2.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.

3.After a 20% discount, a jacket costs £48. Work out the original price of the jacket.

4.Jamal is paid £54 for working 6 hours. Work out his rate of pay, in £ per hour.

5.Divide 84 in the ratio 3:4. Work out the smaller share.

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.£120 is shared between three cousins in the ratio 3:4:5. Work out the largest share.

8.A printer's ink cartridge level, I millilitres, is plotted against the number of pages printed, p, and the points lie on a straight line. The line passes through (0, 24) and (300, 9). The printer has now printed 300 pages. Work out how many more pages it can print before the cartridge is empty.

9.A watering can holds 4500 cm³ of water. Given that 1 litre = 1000 cm³, work out the capacity of the watering can in litres.

10.A garden centre sells two mathematically similar sacks of grass seed. The amount of lawn a sack can treat is proportional to the volume of seed inside it. The smaller sack is 20 cm tall and treats a lawn of area 30 m². The larger sack is 40 cm tall. A gardener needs to treat a lawn with an area of 500 m² using only the larger sacks. Work out the minimum number of larger sacks needed.

11.Work out the difference between 45% of 70 and 35% of 80.

12.Write £3.60 : £2.40 as a ratio in its simplest form.

13.The value of a motorbike falls by 12% each year. The motorbike is worth £3200 now. Write down the calculation that gives its value after 3 years.

14.There are 2500 electric cars registered in a town. The number is predicted to increase by 6% each year. Work out the predicted number of electric cars after 3 years, to the nearest whole number.

15.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.