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Compound Percentage Change Worksheet

GCSE HigherHard15 questions

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Multipliers

To increase by 10%, multiply by 1.1 (100% + 10% = 110% = 1.1)

To decrease by 10%, multiply by 0.9 (100% − 10% = 90% = 0.9)

For compound changes, multiply successive multipliers together. To find the overall % change: combined multiplier − 1, then convert to a percentage.

Apply successive percentage changes using multipliers. Multiply the original by each multiplier in turn. For an overall percentage change, find the combined multiplier, then subtract 1 and convert to a percentage.

  1. Q1. A value increases by 10%, then increases by 10% again. Find the overall percentage change.

  2. Q2. A value increases by 20%, then decreases by 20%. Find the overall percentage change.

  3. Q3. A value increases by 50%, then decreases by 50%. Find the overall percentage change.

  4. Q4. A value decreases by 10%, then decreases by 10% again. Find the overall percentage change.

  5. Q5. A value increases by 25%, then decreases by 20%. Find the overall percentage change.

  6. Q6. A value increases by 30%, then decreases by 15%. Find the overall percentage change.

  7. Q7. A value increases by 40%, then decreases by 30%. Find the overall percentage change.

  8. Q8. A value decreases by 5%, then increases by 5%. Find the overall percentage change.

  9. Q9. A value increases by 15%, then increases by 20%. Find the overall percentage change.

  10. Q10. A value decreases by 20%, then increases by 25%. Find the overall percentage change.

  11. Q11. A price of £200 increases by 10% in year 1, then by 10% in year 2. Find the final price.

  12. Q12. A car worth £12,000 depreciates by 15% in year 1, then by 10% in year 2. Find its value after 2 years.

  13. Q13. A shop increases prices by 20%, then applies a 15% sale reduction. Find the overall percentage change.

  14. Q14. A painting worth £5,000 increases in value by 8% per year for 2 years. Find its value after 2 years.

  15. Q15. An investment of £1,000 grows by 5% in year 1, then by 3% in year 2. Find the final value.

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Worked Answers

  1. Q1. 1.1 × 1.1 = 1.21. Combined multiplier 1.21 means a 21% overall increase.
  2. Q2. 1.2 × 0.8 = 0.96. Combined multiplier 0.96 means a 4% overall decrease.
  3. Q3. 1.5 × 0.5 = 0.75. Combined multiplier 0.75 means a 25% overall decrease.
  4. Q4. 0.9 × 0.9 = 0.81. Combined multiplier 0.81 means a 19% overall decrease.
  5. Q5. 1.25 × 0.8 = 1.0. Combined multiplier 1.0 means no overall change (0%).
  6. Q6. 1.3 × 0.85 = 1.105. Combined multiplier 1.105 means a 10.5% overall increase.
  7. Q7. 1.4 × 0.7 = 0.98. Combined multiplier 0.98 means a 2% overall decrease.
  8. Q8. 0.95 × 1.05 = 0.9975. Combined multiplier 0.9975 means a 0.25% overall decrease.
  9. Q9. 1.15 × 1.2 = 1.38. Combined multiplier 1.38 means a 38% overall increase.
  10. Q10. 0.8 × 1.25 = 1.0. Combined multiplier 1.0 means no overall change (0%).
  11. Q11. £200 × 1.1 × 1.1 = £200 × 1.21 = £242
  12. Q12. £12,000 × 0.85 × 0.90 = £12,000 × 0.765 = £9,180
  13. Q13. 1.2 × 0.85 = 1.02. Combined multiplier 1.02 means a 2% overall increase.
  14. Q14. £5,000 × 1.08² = £5,000 × 1.1664 = £5,832
  15. Q15. £1,000 × 1.05 × 1.03 = £1,000 × 1.0815 = £1,081.50

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