Ratio, proportion and rates of change worksheet — GCSE Foundation

1.A box holds 80 chocolates. 75% of them are milk chocolates. Work out how many milk chocolates are in the box.

2.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.

3.A map has a scale of 2 cm : 5 km. A footpath measures 8 cm on the map. Work out the real length of the footpath, in kilometres.

4.Three business partners share a profit of £48,000 in the ratio 3:5:4. Work out how much the partner with 5 parts receives.

5.A garden centre sells two mathematically similar sacks of grass seed. The amount of lawn a sack can treat is proportional to the volume of seed inside it. The smaller sack is 20 cm tall and treats a lawn of area 30 m². The larger sack is 40 cm tall. A gardener needs to treat a lawn with an area of 500 m² using only the larger sacks. Work out the minimum number of larger sacks needed.

6.A concert hall has 54 seats in total, of which 24 are reserved and the rest are free. Write the number of free seats as a fraction of the number of reserved seats. Give your answer in its simplest form.

7.The same jumper is sold at two shops. Shop A charges £40 and Shop B charges £50. Write down the price at Shop A as a percentage of the price at Shop B.

8.A cartographer is choosing a scale for a map to show a small park in as much detail as possible. Which of these scales would show the MOST detail — 1 : 500, 1 : 5000, or 1 : 50 000? Give the correct scale and reason.

9.A cleaning solution is made by mixing disinfectant and water in the ratio 1 : 9. Priti wants to make 6 litres of the solution in total. Work out how much disinfectant she needs.

10.A film runs for 2.25 hours. Work out the length of the film in minutes.

11.A room is drawn on a plan with a scale of 1 : 200. On the plan the room has an area of 12 cm². Work out the real area of the room, in square metres.

12.A concrete mix is made from gravel and cement in the ratio 5 : 1 by mass. The mass of cement is c kg and the total mass of the mix is m kg. Write down a formula for m in terms of c.

13.Cheng is paid an hourly rate that is proportional to the number of hours she works. She earns £52.50 for 7 hours. Work out how much she earns for 11 hours, assuming the same rate.

14.Two mathematically similar cylinders have heights in the ratio 3 : 4. Write the ratio of their volumes in its simplest form.

15.Square P has sides of length 3 cm. Square Q has sides of length 12 cm. Write the ratio of the area of square P to the area of square Q in its simplest form.