Ratio, proportion and rates of change worksheet — GCSE Foundation

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

2.Write 1/5 as a percentage.

3.6 identical printers can print a batch of exam papers in 40 minutes, all working at the same rate. Working at the same rate, work out how many minutes 4 of these printers would take to print the same batch.

4.y is directly proportional to x. When x = 7, the value of y is 21. Work out the value of x when y = 12.

5.A metal has a density of 7.8 g/cm³. Work out the density of the metal in kg/m³.

6.A machine fills bottles at a constant rate. It fills 18 bottles in 3 minutes. Working at the same rate, work out how many bottles the machine fills in 8 minutes.

7.Isla and her brother share £60 in the ratio 1:2. Work out Isla's share.

8.A section of a kitchen wall has an area of 45,000 cm². Work out the area of this section in m².

9.Write 0.25 as a percentage.

10.A science technician mixes 400 g of a salt solution of concentration 5% with 100 g of a salt solution of concentration 25%. Work out the concentration of the mixture.

11.A room plan is drawn to a scale of 1 : 50. A wall in the room is 4 m long in real life. Work out the length of the wall on the plan, in centimetres.

12.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.

13.A tin of beans has a mass of 400 g. A tin of soup has a mass of 500 g. Write the mass of the tin of beans as a fraction of the mass of the tin of soup, giving your answer in its simplest form.

14.Simplify the ratio 45 : 30 : 75 to its simplest form.

15.In a car park there are 35 cars and 15 vans. Write the ratio of the number of vans to the number of cars in its simplest form.