Ratio, proportion and rates of change worksheet — GCSE Foundation

1.x is 2/3 of y. Write the ratio x : y in its simplest form.

2.A map has a scale of 1 : 20 000. A different map of the same area has a scale of 1 : 80 000. A lake's shoreline is drawn 5 cm long on the first map. Work out the length of the same shoreline on the second map, in centimetres.

3.A river 120 km long is drawn as a line 6 cm long on a map. Work out the scale of the map.

4.A 1.5 kg bag of pasta costs £2.85 and a 2.4 kg bag of the same pasta costs £4.32. Work out which bag gives better value for money.

5.A water butt is being filled from a hosepipe at a constant rate while a small leak drains water out at a constant rate, giving a constant net rate of change. The volume of water in the butt, V litres, is shown on a straight-line graph against time, t minutes. The line passes through the points (5, 20) and (15, 60). The butt is empty at t = 0. Work out how many minutes it takes to reach a volume of 100 litres.

6.Two cars leave the same point at the same time and travel in opposite directions. One travels at 80 km/h and the other at 60 km/h. Work out how long it takes until the cars are 350 km apart.

7.In a fruit drink, 3/8 of the total volume is orange juice and the rest is apple juice. Write down the ratio of orange juice to apple juice, in its simplest form.

8.A recipe for 8 people needs 320 g of rice. Sanjay scales the recipe down to serve 5 people, then wants to scale his new amount back up to serve 8 people again. Work out the multiplier he should use to scale his amount for 5 people back up to the amount for 8 people.

9.A map's scale is given as '1 cm represents 2 km'. Write this scale in the form 1 : n.

10.300 g of a salt solution of concentration 10% is poured into 200 g of a salt solution of concentration 25%. Work out the concentration of salt in the mixture.

11.A shop buys a bike for £150 and sells it, making a profit of £45. Write the selling price as a fraction of the cost price, giving your answer in its simplest form.

12.Two investors put money into a business in the ratio 3:5. The first investor puts in £1,200. Work out the total amount invested by both investors.

13.A cyclist rides at a steady speed of 20 mph. Given that 1 mile ≈ 1.6 km, work out the cyclist's speed in km/h.

14.A train travels at a constant speed of 90 km/h. Work out the speed in m/s.

15.Two numbers A and B are in the ratio 3:5. When 6 is added to B, the ratio of A to the new value of B is 1:2. Work out the value of A.