Ratio, Proportion & Rates of Change
5 free practice questions with explanations
PassNova has 5 free GCSE Maths Higher practice questions on Ratio, Proportion & Rates of Change, each with a clear explanation. Practise them in the browser with instant feedback — 100% free, no sign-up, on any device. Updated for 2026.
Ratio, Proportion & Rates of Change: example questions & answers
5 worked examples with answers and explanations below. Practise them in the browser with instant feedback on every answer.
A car costing £8,000 depreciates by 10% in a year. What is it worth after one year?
- A£7,200✓
- B£800
- C£7,900
- D£8,800
Answer: 10% of £8,000 = £800. £8,000 − £800 = £7,200 (or 0.9 × £8,000).
£500 is invested at 4% simple interest per year. How much interest is earned in 3 years?
- A£20
- B£60✓
- C£600
- D£540
Answer: Simple interest = 0.04 × 500 × 3 = £60.
y is directly proportional to x, and y = 12 when x = 4. Find y when x = 7.
- A21✓
- B19
- C28
- D15
Answer: y = kx; 12 = k×4 so k = 3. When x = 7, y = 3 × 7 = 21.
Increase £80 by 15%.
- A£92✓
- B£95
- C£68
- D£104
Answer: 15% of 80 = 12. £80 + £12 = £92 (or 1.15 × 80).
A price of £60 includes 20% VAT. What was the price before VAT?
- A£48
- B£50✓
- C£40
- D£72
Answer: £60 is 120% of the original. Original = 60 ÷ 1.2 = £50.