GCSE Ratio and Proportion (Foundation Maths) 2 — Questions and Answers
Question 1: It takes 6 workers 8 days to build a wall. Working at the same rate, how long would it take 4 workers?
- 5.33 days
- 6 days
- 10 days
- 12 days (Correct answer)
Correct answer: 12 days
This is inverse proportion. Total work = 6 × 8 = 48 worker-days. 48 ÷ 4 = 12 days.
When two quantities are inversely proportional, as one increases the other decreases so that their product is constant. The job needs 6 × 8 = 48 worker-days in total. With 4 workers, the number of days is 48 ÷ 4 = 12. A common mistake is to treat this as direct proportion and scale the days down, which would wrongly give 5.33 days.
Question 2: Increase 80 by 15%.
- 92 (Correct answer)
- 95
- 68
- 88
Correct answer: 92
15% of 80 is 12, so 80 + 12 = 92. Alternatively, 80 × 1.15 = 92.
A percentage increase can be calculated with a multiplier: increasing by 15% means multiplying by 100% + 15% = 115% = 1.15. So 80 × 1.15 = 92. You can also find 10% of 80 (8) and 5% of 80 (4), add them to get 12, and add that to 80. The answer 68 is what you would get if you decreased 80 by 15% instead.
Question 3: A jacket costs £45 in a sale after a 25% reduction. What was the original price?
- £56.25
- £60 (Correct answer)
- £33.75
- £70
Correct answer: £60
£45 is 75% of the original price, so original = 45 ÷ 0.75 = £60.
After a 25% reduction, the sale price is 100% − 25% = 75% of the original, so the multiplier is 0.75. To reverse it, divide the sale price by the multiplier: 45 ÷ 0.75 = 60. Check: 25% of £60 is £15, and £60 − £15 = £45. Adding 25% to £45 (giving £56.25) is a common error because the 25% was taken from the original price, not the sale price.
Question 4: A map has a scale of 1 : 50 000. Two towns are 6 cm apart on the map. What is the real distance between them?
- 300 m
- 3 km (Correct answer)
- 30 km
- 300 km
Correct answer: 3 km
6 cm × 50 000 = 300 000 cm = 3000 m = 3 km.
A scale of 1 : 50 000 means 1 cm on the map represents 50 000 cm in real life. So 6 cm represents 6 × 50 000 = 300 000 cm. Converting units: 300 000 cm ÷ 100 = 3000 m, and 3000 m ÷ 1000 = 3 km. Always convert the final answer into a sensible unit and show your unit conversions clearly.
Question 5: Which of the following is the best value for money?
- 500 g of pasta for £1.00
- 750 g of pasta for £1.40
- 1 kg of pasta for £1.90
- 2 kg of pasta for £3.70 (Correct answer)
Correct answer: 2 kg of pasta for £3.70
Cost per kg: A = £2.00, B ≈ £1.87, C = £1.90, D = £1.85. The 2 kg pack is cheapest per kg.
To compare value, work out the cost of the same amount for each option. Per kilogram: 500 g for £1.00 is £2.00/kg; 750 g for £1.40 is 1.40 ÷ 0.75 ≈ £1.87/kg; 1 kg for £1.90 is £1.90/kg; 2 kg for £3.70 is 3.70 ÷ 2 = £1.85/kg. The lowest cost per kilogram is the 2 kg pack, so it is the best value.
Question 6: A car travels 210 miles using 6 gallons of fuel. At the same rate, how far can it travel on 10 gallons?
- 300 miles
- 320 miles
- 350 miles (Correct answer)
- 360 miles
Correct answer: 350 miles
210 ÷ 6 = 35 miles per gallon. 35 × 10 = 350 miles.
Distance is directly proportional to the amount of fuel used at a constant rate. Find the unit rate: 210 miles ÷ 6 gallons = 35 miles per gallon. Then multiply by 10 gallons: 35 × 10 = 350 miles. Rates like miles per gallon, price per kilogram and metres per second all follow this same unitary approach.
GCSE Ratio and Proportion (Foundation Maths) 2
It takes 6 workers 8 days to build a wall.
Working at the same rate, how long would it take 4 workers?