Ratio, proportion and rates of change worksheet — GCSE Foundation

1.A pump fills a paddling pool at a rate of 130 litres per hour. Work out the rate in litres per minute, to 2 decimal places.

2.A recipe uses flour and sugar in the ratio 4 : 1 by mass. The mass of sugar is s grams and the mass of flour is f grams. Write down a formula for f in terms of s.

3.Grace's mean mark in her maths tests rises from 70 to 84. Work out the percentage increase in her mean mark.

4.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.

5.A train travels at a constant speed of 90 km/h. Work out the speed in m/s.

6.A map's scale is given as '1 cm represents 2 km'. Write this scale in the form 1 : n.

7.A map has a scale of 1:25000. A road on the map is 6 cm long. Work out the real-life length of the road, giving your answer in kilometres.

8.Rice costs £3.20 per kg. Work out the cost of the rice in pence per 100 g.

9.y is inversely proportional to x, and y = 20 ÷ x. Work out the value of y when x = 4.

10.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.

11.Two mathematically similar jugs have heights 8 cm and 12 cm. The smaller jug holds 200 ml when it is full. Work out how much the larger jug holds when it is full.

12.Two numbers are in the ratio 3 : 7. Their sum is 60. Work out the positive difference between the two numbers.

13.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.

14.A water butt is being filled from a hosepipe at a constant rate while a small leak drains water out at a constant rate, giving a constant net rate of change. The volume of water in the butt, V litres, is shown on a straight-line graph against time, t minutes. The line passes through the points (5, 20) and (15, 60). The butt is empty at t = 0. Work out how many minutes it takes to reach a volume of 100 litres.

15.The ratio of the amount of money Harry has to the amount of money Isla has is 5:3. Harry has £35. Work out how much money Isla has.