Ratio, proportion and rates of change worksheet — GCSE Foundation

1.Two cars leave the same point at the same time and travel in opposite directions. One travels at 80 km/h and the other at 60 km/h. Work out how long it takes until the cars are 350 km apart.

2.£96 is shared between Ben, Cara and Dev in the ratio 2:3:7. Work out how much Cara receives.

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

4.Order these three values from smallest to largest: 3/8, 0.43, 41%.

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

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

7.Two broadband providers show their monthly cost on straight-line graphs, with the cost in pounds on the vertical axis and the data used in gigabytes on the horizontal axis. Provider X's line passes through (0, 15) and (100, 35). Provider Y's line passes through (0, 5) and (100, 45). Work out which provider is cheaper for a customer who uses 40 gigabytes in a month.

8.The ratio of two lengths is 0.6 : 1.5. Write this ratio in its simplest whole-number form.

9.A garden plan is enlarged by a scale factor of 3. A flower bed on the original plan is 5 cm long. Work out the length of the flower bed on the enlarged plan, in centimetres.

10.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.

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

12.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.

13.A jumper costs £45 at Shop A, where it is reduced by 20%. The same jumper costs £34 at Shop B, where a further 10% reduction is then applied. Work out the difference between the two reduced prices.

14.y is directly proportional to x, and y = 7x. Work out the value of x when y = 35.

15.In a science lesson Priya has 10 litres of a solution that is 30% salt. She adds water to make a solution that is 20% salt. Work out how many litres of water she adds.