Ratio, proportion and rates of change worksheet — GCSE Foundation

1.x × y is used to test whether two quantities are in inverse proportion. For the pairs x = 4, y = 15 and x = 6, y = 10, which statement is correct?

2.6 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.

3.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.

4.A glass holds 250 ml of squash. Work out how many of these glasses are needed to fill a 1 litre bottle.

5.A box contains 12 red counters and 18 blue counters. Write the number of red counters as a fraction of the number of blue counters. Give your answer in its simplest form.

6.A ratio is 3 : 5. Write the first part of the ratio as a fraction of the whole.

7.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.

8.A journey to school takes 12 minutes. A journey to the gym takes 20 minutes. Write the time for the journey to school as a fraction of the time for the journey to the gym, giving your answer in its simplest form.

9.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.

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

11.Write the ratio 6a : 9a in its simplest form, where a is a positive number.

12.A recipe for pastry uses flour and butter in the ratio 3:2. A baker has 180 g of butter and wants to make pastry using all of it. Work out the total mass of pastry the baker can make.

13.It takes 8 painters 6 days to paint a fence. Working at the same rate, work out how many days 4 painters would take to paint the same fence.

14.A recipe for 6 muffins needs 150 g of flour. Aisha wants to make 15 muffins using the same recipe. Work out how much flour she needs.

15.A recipe requires flour and butter in the ratio 3 : 2. Write down which of these amounts could be used in the recipe.