Ratio, proportion and rates of change worksheet — GCSE Foundation

1.A map has a scale of 1 : 1000. A road is 300 m long in real life. Work out the length of the road on the map, in centimetres.

2.A road sign 3 m tall casts a shadow 5 m long. At the same time, a nearby lamppost casts a shadow 10 m long. Work out the height of the lamppost.

3.The number of members of a running club increases from 45 to 54. Work out the percentage increase.

4.Two printers' running costs are shown on separate straight-line graphs of total cost against number of pages printed. Printer A's graph has gradient £0.04 per page. Printer B's graph has gradient £0.05 per page. Work out how much cheaper it is to print 200 pages on Printer A than on Printer B, based on these running costs alone.

5.y is inversely proportional to x, and y = 20 ÷ x. Work out the value of y when x = 4.

6.A map has a scale of 1 : 40 000. A cycle path measures 7.5 cm on the map. Work out the real length of the cycle path, in kilometres.

7.Jamal is paid £54 for working 6 hours. Work out his rate of pay, in £ per hour.

8.6 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.

9.The ratio of the amount of money Harry has to the amount of money Isla has is 5:3. Harry has £35. Work out how much money Isla has.

10.Write 0.25 as a percentage.

11.Amelia uses 2 kg of flour to bake 5 cakes. Using the same recipe, work out how many cakes she can bake with 6 kg of flour.

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

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

14.40% of a number is 12 more than 25% of the same number. Work out the number.

15.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?