Ratio, proportion and rates of change worksheet — GCSE Foundation

1.A company's turnover this year is £180,000. Last year's turnover was £120,000. Write down this year's turnover as a percentage of last year's turnover.

2.A cyclist rides 17.5 km on Saturday and 12.25 km on Sunday. Write the distance ridden on Saturday as a fraction of the distance ridden on Sunday, giving your answer in its simplest form.

3.In a fruit bowl, the ratio of apples to oranges is 5 : 3. Work out what percentage of the fruit in the bowl is apples.

4.A shop buys a bike for £150 and sells it, making a profit of £45. Write the selling price as a fraction of the cost price, giving your answer in its simplest form.

5.The ratio of the amount of money Harry has to the amount of money Isla has is 5:3. Harry has £35. Work out how much money Isla has.

6.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.

7.A photo is enlarged so that its new width is 1.4 times its original width. Write the multiplier that would scale the new width back down to the original width, as a fraction in its simplest form.

8.A colony of bacteria has 400 bacteria. The number increases by 15% each hour. Work out the number of bacteria after 1 hour.

9.Write 45 minutes : 2 hours as a ratio in its simplest form.

10.A coach journey is 372 miles in total. After a stop, the coach has travelled 217 miles. Write the distance still to travel as a fraction of the total journey. Give your answer in its simplest form.

11.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.

12.It takes 8 painters 6 days to paint a fence. Working at the same rate, work out how many days 4 painters would take to paint the same fence.

13.Two printers' running costs are shown on separate straight-line graphs of total cost against number of pages printed. Printer A's graph has gradient £0.04 per page. Printer B's graph has gradient £0.05 per page. Work out how much cheaper it is to print 200 pages on Printer A than on Printer B, based on these running costs alone.

14.Freya buys three items whose prices are in the ratio 2:3:5. Altogether she pays £400. Work out the price of the most expensive item.

15.Work out 50% of 60.