Ratio, proportion and rates of change worksheet — GCSE Foundation

1.Two cars travel at constant speeds. Car A travels 150 km in 3 hours. Car B travels 180 km in 4 hours. Which car is faster, and what is its speed?

2.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.

3.A smoothie recipe combines 350 cm³ of mango juice with 650 cm³ of orange juice. Work out the total volume of the smoothie in litres.

4.A machine fills bottles at a constant rate. It fills 18 bottles in 3 minutes. Working at the same rate, work out how many bottles the machine fills in 8 minutes.

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

6.A metal alloy is made from copper and tin in the ratio 9:1. Write the mass of tin as a fraction of the mass of copper, in its simplest form.

7.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.

8.In a choir of 30 singers, 40% are altos and the rest are sopranos. Write the number of sopranos as a fraction of the number of altos. Give your answer in its simplest form.

9.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.

10.A cyclist travels 18 km in 45 minutes. Work out the average speed, in km/h.

11.y is directly proportional to x. When x = 4, y = 10. Work out the value of y when x = 6.

12.Two numbers are in the ratio 5 : 8. The larger number is 40. Work out the smaller number.

13.Given that 1 mile ≈ 1.6 km, work out a speed of 55 mph in km/h.

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

15.Two mathematically similar cylinders have heights in the ratio 3 : 4. Write the ratio of their volumes in its simplest form.