Ratio Proportion and Rates

Simplify the ratio 12:8.

• A6:4
• B3:2✓
• C12:8
• D4:3

Answer: Divide both by HCF(12, 8) = 4: 12:8 = 3:2.

Simplify the ratio 15:25.

• A5:8
• B3:5✓
• C15:25
• D6:10

Answer: HCF(15, 25) = 5: 15:25 = 3:5.

Share £30 in the ratio 2:3.

• A£10 and £20
• B£12 and £18✓
• C£15 and £15
• D£20 and £10

Answer: Ratio 2:3 means 5 parts total. £30 ÷ 5 = £6 per part. 2 parts = £12, 3 parts = £18.

A car travels 120 miles in 2 hours. What is its average speed?

• A50 mph
• B60 mph✓
• C70 mph
• D80 mph

Answer: Speed = distance ÷ time = 120 ÷ 2 = 60 mph.

If 3 apples cost 90p, how much do 5 apples cost?

• A150p✓
• B130p
• C180p
• D120p

Answer: Cost per apple = 90p ÷ 3 = 30p. 5 apples = 5 × 30p = 150p.

A recipe uses flour and sugar in the ratio 4:1. If there are 400g of flour, how much sugar is needed?

• A100g✓
• B200g
• C400g
• D1600g

Answer: Ratio 4:1 means for every 4g flour, 1g sugar is needed. 400g ÷ 4 = 100g sugar.

A train travels 180 km in 3 hours. What is its speed?

• A40 km/h
• B50 km/h
• C60 km/h✓
• D70 km/h

Answer: Speed = 180 ÷ 3 = 60 km/h.

Share 24 sweets in the ratio 1:2.

• A8 and 16✓
• B10 and 14
• C12 and 12
• D6 and 18

Answer: Ratio 1:2 means 3 parts total. 24 ÷ 3 = 8 per part. 1 part = 8, 2 parts = 16.

If 10 litres of paint cover 50 m², how much paint is needed to cover 75 m²?

• A10 litres
• B15 litres✓
• C20 litres
• D25 litres

Answer: Paint needed per m² = 10 ÷ 50 = 0.2 litres. For 75 m² = 75 × 0.2 = 15 litres.

Simplify 20:30:10.

• A2:3:1✓
• B10:15:5
• C20:30:10
• D4:6:2

Answer: HCF(20, 30, 10) = 10: 20:30:10 = 2:3:1.

A cyclist travels 24 km in 2 hours. What is the speed?

• A10 km/h
• B12 km/h✓
• C14 km/h
• D24 km/h

Answer: Speed = 24 ÷ 2 = 12 km/h.

In a school, the ratio of boys to girls is 3:2. If there are 60 boys, how many girls are there?

• A30
• B40✓
• C50
• D90

Answer: Ratio 3:2 means 3 boys for every 2 girls. If 3 parts = 60, then 1 part = 20. Girls = 2 × 20 = 40.