Ratio, proportion and rates of change worksheet — GCSE Foundation

1.Two quantities x and y are inversely proportional. When x = 2, the value of y is 15. Work out the value of y when x = 5.

2.Two numbers are in the ratio 2 : 3. The smaller number is 8. Work out the larger number.

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

4.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.

5.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.

6.Three numbers are in the ratio 1:2:3. The three numbers add up to 72. Work out the largest of the three numbers.

7.A car travels 90 km using 6 litres of petrol. Work out how far the car can travel, at the same rate, using 9 litres of petrol.

8.Write 350 ml : 1.4 l as a ratio in its simplest form.

9.A straight-line graph passes through the origin and the point (4, 10). The line represents y = kx. Write down the ratio x : y in its simplest form.

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

11.In a school choir the ratio of boys to girls is 3:4. When 6 more boys join the choir, the ratio of boys to girls becomes 1:1. Work out how many girls are in the choir.

12.Order these three values from smallest to largest: 3/8, 0.43, 41%.

13.Two mathematically similar logos are printed on a poster. They have areas 20 cm² and 45 cm². Nadia says that the length scale factor from the smaller logo to the larger logo is 45 ÷ 20 = 2.25. Give a reason why Nadia is incorrect, and work out the correct length scale factor.

14.In a fruit drink, 3/8 of the total volume is orange juice and the rest is apple juice. Write down the ratio of orange juice to apple juice, in its simplest form.

15.3 kg of apples cost £6. Work out the cost of 5 kg of the same apples.