Ratio, proportion and rates of change worksheet — GCSE Foundation

1.Write 75p : £1.50 as a ratio of whole numbers in its simplest form.

2.Two quantities x and y are in the ratio x : y = 2 : 5, and y = kx for a constant k. Work out the value of k.

3.£2000 is invested in a savings account that pays 5% compound interest each year. Work out the value of the investment at the end of 2 years.

4.A cyclist rides at an average speed of 24 km/h for 1 hour 15 minutes. Work out the distance travelled, in km.

5.A recipe for 4 people needs 300 g of rice. Work out how much rice is needed for 6 people, assuming the amount is in direct proportion to the number of people.

6.Work out how many seconds there are in 3 minutes and 20 seconds.

7.A map's scale is given as '1 cm represents 2 km'. Write this scale in the form 1 : n.

8.Work out 25% of 200.

9.A garden centre has 90 rose bushes in stock. It receives a delivery that increases its stock of rose bushes by 20%. In the same week it sells 150 lavender bushes. Work out the new number of rose bushes, then write it as a fraction of the number of lavender bushes sold, giving your answer in its simplest form.

10.At a youth club the ratio of juniors to seniors is 3:5. There are 40 members altogether. Work out how many seniors there are.

11.Tap A fills a swimming pool in 6 hours. Tap B pours water twice as fast as tap A. The time taken to fill the pool is inversely proportional to the rate of flow. Work out how long tap B takes to fill the pool.

12.Aisha invests £3200 in Account A, which pays 5% compound interest each year. She also invests £3200 in Account B, which pays 3% simple interest each year. Work out how much more Account A is worth than Account B after 2 years.

13.For the pairs x = 6, y = 15 and x = 10, y = 25, which statement is correct?

14.Two mathematically similar rectangles have lengths in the ratio 3 : 5. The area of the smaller rectangle is 27 cm². Work out the area of the larger rectangle.

15.Maya buys a vintage car for £15000. Its value is expected to increase by 4% each year for 2 years. She then plans to sell the car and use £2000 of the money from the sale to buy a trailer. Work out how much money she will have left after selling the car and buying the trailer.