Ratio, proportion and rates of change worksheet — GCSE Foundation

1.Two numbers a and b are in the ratio a : b = 3 : 4. Given that a = 15, work out the value of b.

2.A gardener mixes 300 ml of plant feed concentrate with 1.2 litres of water to make a spray. Write the ratio of concentrate to water in its simplest form.

3.A water tank has a capacity of 500 litres. It currently holds 350 litres of water. Write the amount of empty space in the tank as a fraction of the tank's capacity. Give your answer in its simplest form.

4.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.

5.Write the ratio 4 : 9 in the form 1 : n.

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

7.Which of these ratios is equivalent to 6 : 10 : 14?

8.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.

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

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

11.The population of a village is 1200. It is predicted to grow by 5% next year. Work out the predicted population after 1 year, to the nearest whole number.

12.A map has a scale of 1 : 100. A path measures 5 cm on the map. Work out the real length of the path, in metres.

13.A company's profit this year is 130% of last year's profit. Last year's profit was £40,000. Work out this year's profit.

14.A company's turnover was £128 000 in 2023 and £176 000 in 2024. Work out the multiplier that changes the 2023 turnover into the 2024 turnover.

15.Two mathematically similar hexagonal tiles have areas 18 cm² and 50 cm². Work out the ratio of the side length of the smaller tile to the side length of the larger tile, in simplest form.