Ratio, proportion and rates of change worksheet — GCSE Foundation

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

2.A printer prints at a constant rate. The time taken to print a batch of forms is inversely proportional to the printer's speed, in pages per minute. Printing at 20 pages per minute takes 15 minutes. Work out how long the same batch takes to print at 25 pages per minute. Give your answer in minutes.

3.6 identical taps fill a paddling pool in 20 minutes. Each tap fills at the same steady rate. Work out how long 3 of these taps would take to fill the same pool.

4.y is directly proportional to x. When x = 5, y = 18. Work out the value of y when x = 15.

5.Ffion is paid £11.20 per hour. She works 6 hours on Monday and 4.5 hours on Tuesday. Work out her total pay for the two days.

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

7.The value of a rare coin increases by 12% each year. The coin is currently worth £270. Work out the value of the coin after 2 years, giving your answer to the nearest penny.

8.Two investors put money into a business in the ratio 3:5. The first investor puts in £1,200. Work out the total amount invested by both investors.

9.Jamal invests £600 in a savings account paying 3% simple interest per year. Work out the total amount in the account after 4 years.

10.Water flows into a tank at a constant rate. After 8 minutes the tank holds 200 litres. Write the ratio of time in minutes to volume in litres, in its simplest form.

11.A scale drawing states '1 cm represents 25 m'. Which of these is the correct way to write this scale in the form 1 : n?

12.A map has a scale of 1 : 40 000. A cycle path measures 7.5 cm on the map. Work out the real length of the cycle path, in kilometres.

13.A shop sells rope by the metre. 3 m costs £7.50 and 5 m costs £11.00. Does this data show that the cost is directly proportional to the length of rope bought? Choose the correct verdict and reason.

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

15.Maya is paid £105.30 for working 9 hours. Work out her rate of pay, in £ per hour.