Ratio, proportion and rates of change worksheet — GCSE Foundation

1.Write the ratio 27 : 45 in its simplest form.

2.A factory machine produces bottles at a constant rate. In 45 minutes it produces 810 bottles. The factory needs 2,160 bottles for an order. Working at the same rate, work out how many minutes it will take to produce the order.

3.A garden centre has 90 rose bushes in stock. It receives a delivery that increases its stock of rose bushes by 20%. In the same week it sells 150 lavender bushes. Work out the new number of rose bushes, then write it as a fraction of the number of lavender bushes sold, giving your answer in its simplest form.

4.A map has a scale of 1 : 100. A path measures 5 cm on the map. Work out the real length of the path, in metres.

5.A recipe for 4 people needs 300 g of rice. Work out how much rice is needed for 6 people, assuming the amount is in direct proportion to the number of people.

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

7.A company's turnover this year is £180,000. Last year's turnover was £120,000. Write down this year's turnover as a percentage of last year's turnover.

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

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

10.The price of a cycling helmet rises from £80 to £116. Work out the percentage increase.

11.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.

12.A gym charges members a joining fee plus a fixed amount per month. The total amount paid, C pounds, is shown on a straight-line graph against the number of months, m. The line passes through the points (3, 130) and (7, 210). Work out the total amount a member will have paid after 12 months.

13.A plan is drawn to a scale of 1 : 500. Work out how many metres are represented by 1 cm on the plan.

14.A necklace uses 22 blue beads and 8 red beads. Write the number of blue beads as a fraction of the number of red beads. Give your answer as a mixed number in its simplest form.

15.A garden plan is enlarged by a scale factor of 3. A flower bed on the original plan is 5 cm long. Work out the length of the flower bed on the enlarged plan, in centimetres.