Ratio, proportion and rates of change worksheet — GCSE Foundation

1.y is always the same multiple of x. When x = 6, y = 15. Work out the value of y when x = 10.

2.2.4 kg of cheese costs £36. Work out the cost of 1.5 kg of the same cheese.

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 hosepipe fills a paddling pool at a constant rate. The volume of water in the pool increases by 15 litres every 3 minutes. Write down the gradient of the graph of volume against time.

5.Write the ratio 2 : 1/4 as a ratio of whole numbers in its simplest form.

6.At an animal shelter, the ratio of cats to dogs is 2:5. There are 18 more dogs than cats. Work out the number of cats.

7.In a choir of 30 singers, 40% are altos and the rest are sopranos. Write the number of sopranos as a fraction of the number of altos. Give your answer in its simplest form.

8.A plan of a garden is drawn to a scale of 1 : 200. A path measures 3 cm on the plan. Work out the real length of the path, in centimetres.

9.Two numbers A and B are in the ratio 3:5. When 6 is added to B, the ratio of A to the new value of B is 1:2. Work out the value of A.

10.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.

11.In a bag the ratio of red counters to blue counters is 7 : 4. Write the number of red counters as a fraction of the number of blue counters.

12.In a fruit drink, 3/8 of the total volume is orange juice and the rest is apple juice. Write down the ratio of orange juice to apple juice, in its simplest form.

13.A journey takes 4 hours at an average speed of 60 km/h. The time taken is inversely proportional to the average speed. Work out how long the same journey takes at an average speed of 80 km/h.

14.The density of a liquid is 0.92 g/cm³. Work out the density of the liquid in kg/m³.

15.A vegetable patch is divided between carrots, potatoes and onions in the ratio 2 : 3 : 5. Write down the fraction of the patch used for potatoes.