Ratio, proportion and rates of change worksheet — GCSE Foundation

1.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.

2.Sam has £24. Tom has £16. Write the amount of money Sam has as a fraction of the amount of money Tom has, giving your answer in its simplest form.

3.A film lasts 105 minutes. A documentary lasts 45 minutes. Write the length of the film as a fraction of the length of the documentary. Give your answer in its simplest form.

4.5 tins of soup cost £8 in total. Work out the multiplier that changes the number of tins into the total cost in pounds.

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

6.The ratio of y to x is always 3 : 4. Write down which equation could represent this relationship.

7.A plan is drawn to a scale of 1 : 500. Work out how many metres are represented by 1 cm on the plan.

8.A bag contains 7 red counters and 15 blue counters. Write down the ratio of red counters to blue counters in its simplest form.

9.A scale drawing of a playground is drawn to a scale of 1 : 300. A slide measures 4 cm on the drawing. Work out the real length of the slide, in centimetres.

10.The price of a share falls by 10% on Monday and then rises by 10% on Tuesday. Work out the overall percentage change from Monday's starting price.

11.A toy manufacturer makes a model aircraft that is mathematically similar to the real aircraft, at a scale of 1 : 48. The wingspan of the model is 15 cm. Work out the wingspan of the real aircraft, giving your answer in metres.

12.A recipe for 8 muffins needs 200 g of sugar. Sam wants to make 20 muffins for a bake sale, and he already has 350 g of sugar. Work out how many more grams of sugar he needs to buy.

13.A laptop is bought for £600. Its value decreases by 20% after 1 year. Work out the value of the laptop after 1 year.

14.Write the ratio 5 : 8 in the form 1 : n.

15.A straight-line graph shows the cost, C pounds, of hiring a small van for m miles driven. The line passes through the origin and the point (25, 20). Work out the gradient of the line.