GCSE Maths Ratio & scale questions by topic

Simplifying ratios.

1. (a)Write 18 : 24 in its simplest form.[1]
2. (b)Write 75 p : £3 in its simplest form.[2]
3. (c)Write 12 g as a fraction of 40 g, in its simplest form.[1]

Sharing money.

1. (a)Share £88 in the ratio 2 : 6.[3]
2. (b)Write the larger share as a fraction of the whole.[1]

A squash drink is mixed with water in the ratio 1 : 4.

1. (a)How much squash is needed for 500 ml of water?[2]
2. (b)How much drink does 60 ml of squash make in total?[2]

Scale drawings.

1. (a)A plan has scale 1 : 50. A wall measures 12 cm on the plan. Find the real length in metres.[2]
2. (b)A real football pitch is 90 m long. How long is it on a 1 : 500 plan, in centimetres?[2]

A crumble is weighed out in three parts.

1. (a)A crumble topping mixes flour, butter and sugar in the ratio 6 : 4 : 3. Work out the total number of parts.[1]
2. (b)A crumble uses 260 g of topping in total. Work out the weight of each ingredient.[3]

Walking a map route at two scales.

1. (a)A map has scale 1 : 50 000. Work out the real distance for 5 cm on the map, in kilometres.[2]
2. (b)A different walk is 3.5 km long. Work out its length on the map, in centimetres.[2]

Ratios with three parts and a reverse step.

1. (a)Share 480 g of trail mix in the ratio 5 : 2 : 1 (nuts : fruit : chocolate).[3]
2. (b)The fruit and chocolate together weigh 72 g in a smaller bag with the same ratio. Find the total weight of the smaller bag.[2]

Best buys.

1. (a)Washing powder: 2 kg for £8 or 3 kg for £11.40. Which is better value? Show unit prices.[3]
2. (b)How much does 5 kg cost at the better unit price?[1]

Ratio to fraction and back.

1. (a)In a class the ratio of left-handed to right-handed students is 2 : 7. What fraction of the class is left-handed?[2]
2. (b)There are 28 right-handed students. How many students are left-handed?[2]

Mixing to order.

1. (a)Punch mixes orange : mango : lemonade in the ratio 3 : 1 : 4. How much mango is needed for 4 litres of punch?[2]
2. (b)A jug has 1.5 litres of orange. How much lemonade keeps the ratio?[2]

Savings differ by a known amount.

1. (a)Two sisters save in the ratio 5 : 3, and the older has £24 more. Work out how much each has saved.[3]
2. (b)Work out their total savings.[1]

Tea bags are compared across three boxes.

1. (a)Box A has 80 tea bags for £2.40 and box B has 60 for £1.98. Work out the cost per bag of each box, in pence.[2]
2. (b)State which box is the better buy.[1]
3. (c)Box C offers 100 bags for £3.30. Explain whether it beats box A.[2]

Ratio before and after. (Higher)

1. (a)A necklace has beads in the ratio gold : silver = 5 : 3. There are 36 silver beads. How many gold beads are there?[2]
2. (b)How many beads in total?[1]
3. (c)Six gold beads are replaced by silver. Write the new ratio gold : silver in its simplest form.[3]

Scale and area. (Higher)

1. (a)A scale drawing uses 1 : 200. A room is 4.2 cm × 3.5 cm on the drawing. Find its real dimensions in metres.[3]
2. (b)Find the real floor area in m².[2]
3. (c)Explain why the drawing area × 200² (not × 200) gives the real area.[1]

A ratio change problem. (Higher)

1. (a)Red and blue counters are in the ratio 4 : 7. There are 63 blue counters. How many counters are there in total?[3]
2. (b)Twelve red counters are removed. Write the new ratio red : blue in its simplest form.[3]

A map and a model combined. (Higher)

1. (a)On a 1 : 25 000 map, a path measures 8.2 cm. Find the real length in kilometres.[2]
2. (b)A walker covers that distance in 2 hours. Find their average speed in km/h.[1]
3. (c)A 1 : 500 model of the same path is built. How long is the model path in centimetres?[2]
4. (d)Explain why the model is longer than the 8.2 cm map drawing.[2]

Counters are added and the ratio shifts. (Higher)

1. (a)A jar holds red and yellow counters in the ratio 2 : 3. Twelve red counters are added, and the ratio becomes 4 : 3. Show that the original jar held 12 red counters.[3]
2. (b)Find the original number of yellow counters.[1]
3. (c)Verify that 24 : 18 simplifies to 4 : 3.[2]

A route is mapped and modelled. (Higher)

1. (a)A walking map has scale 1 : 20 000. A route measures 4.2 cm on the map. Work out the real distance in kilometres.[2]
2. (b)A scale model of the same route is built at 1 : 500. Work out the length of the model in centimetres.[2]
3. (c)Write the ratio of map length to model length in its simplest form.[2]