Ratio, proportion and rates of change worksheet — GCSE Foundation

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

2.Write the ratio 3/4 : 1/2 as a ratio of whole numbers in its simplest form.

3.A stall sells bottles of juice. Two bottles cost £3.00, five bottles cost £7.50 and eight bottles cost £12.00. The cost, C pounds, is in a fixed ratio to the number of bottles, n. Write down a formula for C in terms of n.

4.The density of a liquid is 0.92 g/cm³. Work out the density of the liquid in kg/m³.

5.An acid solution has a concentration of 20%. The solution contains 40 g of acid, and the rest of the solution is water. Work out the mass of water in the solution.

6.Work out 25% of 200.

7.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.

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

9.There are 84 passengers on a double-decker bus. 35 of the passengers are adults and the rest are children. Write the number of adults as a fraction of the number of children. Give your answer in its simplest form.

10.Write the ratio 4x : 6x in its simplest form, where x is a positive number.

11.Two mathematically similar cubes have edge lengths 2 cm and 6 cm. Write the ratio of the volume of the smaller cube to the volume of the larger cube in its simplest form.

12.8 identical pens cost £6.40 in total. Work out the cost of 5 of the same pens.

13.A straight-line graph shows the number of pages printed, p, plotted against the time in minutes, t, since a printer started a print job. The line passes through the points (2, 30) and (5, 90). Work out the gradient of the line.

14.y is inversely proportional to x. When x = 5, y = 8. Work out the value of y when x = 10.

15.A road sign 3 m tall casts a shadow 5 m long. At the same time, a nearby lamppost casts a shadow 10 m long. Work out the height of the lamppost.