Ratio, proportion and rates of change worksheet — GCSE Foundation

1.A sculptor makes two mathematically similar statues. The smaller statue is 20 cm tall and 80 ml of varnish covers its surface. The larger statue is 50 cm tall. Work out how much varnish is needed to cover the surface of the larger statue.

2.Work out 25% of 200.

3.A dog walker's charge, C pounds, for walking a dog for m minutes is shown on a straight-line graph. The line passes through the points (20, 14) and (50, 26). Work out the charge for a 65-minute walk.

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

5.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.

6.A printer prints at a constant rate. The time taken to print a batch of forms is inversely proportional to the printer's speed, in pages per minute. Printing at 20 pages per minute takes 15 minutes. Work out how long the same batch takes to print at 25 pages per minute. Give your answer in minutes.

7.Zara is paid £9 per hour. Her wage is directly proportional to the number of hours she works. Work out her wage for working 6 hours.

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

9.In a bag the ratio of red counters to blue counters is 7 : 4. Write the number of red counters as a fraction of the number of blue counters.

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

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

12.A jug holds 2 litres. Given that 1 litre = 1000 cm³, work out the capacity of the jug in cm³.

13.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.

14.Two quantities x and y are in direct proportion. When x = 8, the value of y is 20. Work out the value of y when x = 14.

15.The number of calories burned, E, by a runner is plotted against the time, m minutes, on a straight-line graph. The line passes through the origin and the point (10, 80). Work out the gradient of the line.