Ratio, proportion and rates of change worksheet — GCSE Foundation

1.The ratio of the amount Noah has saved to the amount Grace has saved is 4:5. Noah has saved £200. Work out how much they have saved altogether.

2.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.

3.Write 1/5 as a percentage.

4.Freya buys three items whose prices are in the ratio 2:3:5. Altogether she pays £400. Work out the price of the most expensive item.

5.The ratio of the number of pages Mia has read to the number of pages Leo has read is 7 : 4. Mia has read 84 pages. Work out how many pages they have read altogether.

6.A bag contains red counters and blue counters in the ratio 5:3. There are 56 counters in the bag altogether. Work out how many counters are blue.

7.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.

8.The ratio of y to x is always 3 : 4. Write down which equation could represent this relationship.

9.A map has a scale of 1 : 50 000. Two villages are 4 cm apart on the map. Work out the real distance between the villages, in kilometres.

10.A sofa costs £800. Its price is increased by 25%. Work out the new price of the sofa.

11.Two broadband providers show their monthly cost on straight-line graphs, with the cost in pounds on the vertical axis and the data used in gigabytes on the horizontal axis. Provider X's line passes through (0, 15) and (100, 35). Provider Y's line passes through (0, 5) and (100, 45). Work out which provider is cheaper for a customer who uses 40 gigabytes in a month.

12.A recipe for 6 muffins needs 150 g of flour. Aisha wants to make 15 muffins using the same recipe. Work out how much flour she needs.

13.Before a charity campaign, donations were £6400 per month. Donations grew by 8% in the first year after the campaign, and then fell by 3% in the second year as interest faded. Work out the amount donated per month at the end of the second year, to the nearest pound.

14.A furniture maker builds two mathematically similar bookcases. The smaller bookcase is 40 cm tall and uses 2 m² of wood. The larger bookcase is 60 cm tall. Work out the area of wood needed for the larger bookcase, giving your answer in m².

15.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.