Ratio, proportion and rates of change worksheet — GCSE Foundation

1.Noah runs 2 km in 10 minutes. Work out how long he takes to run 5 km at the same speed.

2.A lorry is carrying a load of mass m tonnes. Given that 1 tonne = 1000 kg, write down an expression for the mass of the load in kilograms.

3.Simplify the ratio 12 : 18 : 30 to its simplest form.

4.Simplify the ratio 45 : 30 : 75 to its simplest form.

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

6.A laptop priced at £520 is first increased by 15%, and then the new price is decreased by 20%. Work out the final price of the laptop.

7.Write 400 g : 1.5 kg as a ratio in its simplest form.

8.A recipe for pancakes uses 240 g of flour to make pancakes for 6 people. Work out how many grams of flour are needed to make pancakes for 15 people, using the same recipe.

9.y is inversely proportional to x, and y = 20 ÷ x. Work out the value of y when x = 4.

10.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.

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

12.Two mathematically similar circles have radii 4 cm and 20 cm. Write the ratio of the area of the smaller circle to the area of the larger circle in its simplest form.

13.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.

14.A sum of £150 is divided between Ben and Chloe in the ratio 2:3. Work out Chloe's share.

15.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.