GCSE Maths (AQA) chapter 3: Ratio, proportion and rates of change MCQs with answers

By Team Megalecture · Updated 4 Nov 2026

46 exam-style questions on Ratio, proportion and rates of change, each with the answer and a short explanation. Ten of them are below to try. The chapter test draws ten fresh questions each time and is marked the moment you finish, with your score by topic.

46 questions · 5 topics · 10 per test

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What chapter 3 covers

Ten Ratio, proportion and rates of change questions with answers

Try each one, then open the answer. These ten stay the same; the test draws new ones every time.

1. a : b = 3 : 4 and b : c = 6 : 5. What is a : c in its simplest form?

  1. A
    3 : 5
  2. B
    9 : 10
  3. C
    1 : 2
  4. D
    18 : 15
Show answer

Answer: B. Make b the same in both: a : b = 9 : 12 and b : c = 12 : 10, so a : c = 9 : 10. Just taking the first and last numbers (3 : 5) ignores that b is different in each ratio.

2. Vn+1 = 0.9Vn + 50 and V0 = 1000. Find V2.

  1. A
    950
  2. B
    860
  3. C
    910
  4. D
    905
Show answer

Answer: D. V1 = 0.9 × 1000 + 50 = 950. V2 = 0.9 × 950 + 50 = 855 + 50 = 905. Adding 50 only once, after 0.92, gives 860.

3. Copper has density 8.9 g/cm3. What is the mass of 25 cm3 of copper?

  1. A
    2.81 g
  2. B
    0.356 g
  3. C
    222.5 g
  4. D
    33.9 g
Show answer

Answer: C. Mass = density × volume = 8.9 × 25 = 222.5 g. Dividing either way round gives the other small values.

4. 6 workers take 10 days to build a wall. How long would 4 workers take, working at the same rate?

  1. A
    6.7 days
  2. B
    12 days
  3. C
    15 days
  4. D
    8 days
Show answer

Answer: C. This is inverse proportion: total work = 6 × 10 = 60 worker-days, so 4 workers take 60 ÷ 4 = 15 days. Fewer workers means more days, so 6.7 days cannot be right.

5. In a sale a coat is reduced by 20% and now costs £68. What was the original price?

  1. A
    £85
  2. B
    £81.60
  3. C
    £88.40
  4. D
    £54.40
Show answer

Answer: A. £68 is 80% of the original, so the original is 68 ÷ 0.8 = £85. Adding 20% of £68 gives £81.60, but the 20% was of the original price.

6. Calculator. m is directly proportional to r3. r increases by 20%. By what percentage does m increase?

  1. A
    60%
  2. B
    72.8%
  3. C
    20%
  4. D
    172.8%
Show answer

Answer: B. The multiplier for r is 1.2, so m is multiplied by 1.23 = 1.728, an increase of 72.8%. 3 × 20% = 60% adds instead of multiplying; 172.8% is the new value as a percentage of the old.

7. Calculator. A radioactive sample loses 12% of its mass each year. After how many whole years is less than half of the original mass left?

  1. A
    4
  2. B
    5
  3. C
    6
  4. D
    7
Show answer

Answer: C. 0.885 = 0.528 (still more than half) and 0.886 = 0.464, so 6 years. 50 ÷ 12 ≈ 4 treats the loss as the same amount each year.

8. A price is reduced by 30%, then the reduced price is cut by a further 10%. The final price is £50.40. What was the original price?

  1. A
    £80
  2. B
    £84
  3. C
    £72
  4. D
    £65.52
Show answer

Answer: A. The overall multiplier is 0.7 × 0.9 = 0.63, so the original is 50.40 ÷ 0.63 = £80. Treating it as a single 40% cut gives £84.

9. Which single multiplier gives a decrease of 7.5%?

  1. A
    0.075
  2. B
    0.925
  3. C
    0.75
  4. D
    1.075
Show answer

Answer: B. 100% − 7.5% = 92.5% = 0.925. 0.075 would find the decrease itself, and 1.075 is an increase.

10. F is inversely proportional to the square of d. When d = 3, F = 20. Find F when d = 6.

  1. A
    5
  2. B
    10
  3. C
    80
  4. D
    2.5
Show answer

Answer: A. F = k/d2, so k = 20 × 9 = 180 and F = 180 ÷ 36 = 5. Doubling d divides F by 22 = 4; dividing by 2 gives 10.

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Ways to practise this chapter

Ratio, proportion and rates of change: questions students ask

How many Ratio, proportion and rates of change MCQs are there?

46, each with the answer and a short explanation, across 5 topics: R1–R8 Units, scale and ratio, R9 Percentages, R10, R13 Direct and inverse proportion, R11, R14–R15 Compound measures and rates of change, R16 Growth and decay. Every chapter test draws ten of them, so you can take it many times.

Is the GCSE Maths (AQA) chapter 3 test free?

Yes. The test, the answers and the explanations are free and need no sign-up. Sign in only if you want your scores kept across devices.

How is the chapter test marked?

The moment you press Finish: your score, the right answer and an explanation for every question, and the ones you got wrong saved in My mistakes to retry.

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