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Percentage Word Problems Worksheet (GCSE)

GCSE | Years 10-11GCSE Exam Style25 questions

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  1. 1. A jacket costs £72 after a 20% reduction. Find the original price.[3 marks]
  2. 2. A shop buys goods for £360 and sells them for £432. Calculate the percentage profit.[3 marks]
  3. 3. After a 15% pay rise, a salary is £34,500. Find the original salary.[3 marks]
  4. 4. A television costs £504 including VAT at 20%. Find the price before VAT.[3 marks]
  5. 5. A house increased in value by 8% to £324,000. Find the original value.[3 marks]
  6. 6. £6,000 is invested at 4% compound interest per year for 3 years. Find the total amount at the end of the 3 years.[3 marks]
  7. 7. A school's pupil numbers fell from 1,200 to 1,008. Calculate the percentage decrease.[3 marks]
  8. 8. A restaurant adds a 12.5% service charge to a bill of £84. What is the total bill?[2 marks]
  9. 9. After a 40% reduction, a price is £270. Find the original price.[3 marks]
  10. 10. A car worth £22,000 depreciates by 18% per year. Find its value after 2 years.[4 marks]
  11. 11. A price increases by 15% then decreases by 10%. Starting from £400, find the final price and state the overall percentage change.[4 marks]
  12. 12. A quantity falls by 60% to become 3,200. Find the original quantity.[3 marks]
  13. 13. £8,000 is invested at 5% compound interest per year. How many complete years does it take for the investment to exceed £9,000?[4 marks]
  14. 14. In a sale, all prices are reduced by 35%. A coat costs £97.50 in the sale. Find the original price.[3 marks]
  15. 15. A company's profits rise from £2.4 million to £2.88 million. Calculate the percentage increase.[3 marks]
  16. 16. A farmer's field produces 4,800 kg of wheat. After a drought, production falls by 37.5%. Find the new yield.[3 marks]
  17. 17. A flat was bought for £185,000 and sold 5 years later for £222,000. Calculate the percentage profit.[3 marks]
  18. 18. A price increases by 25% in year 1 and then by a further 20% in year 2. Starting from £800, find the final price and the overall percentage increase.[4 marks]
  19. 19. A worker's hourly pay is £14.80. After a 7.5% increase, what is the new hourly rate? Give your answer to the nearest penny.[2 marks]
  20. 20. The population of a city increases from 340,000 to 391,000. Calculate the percentage increase.[3 marks]
  21. 21. An investment grows from £12,000 to £14,520 in 2 years with compound interest. Find the annual rate of interest.[4 marks]
  22. 22. After VAT at 20% is included, a bill is £108. How much VAT was charged?[3 marks]
  23. 23. A shop increases a price by 10% and then reduces the new price by 10%. A student says the price is unchanged. Show whether the student is correct.[3 marks]
  24. 24. A savings account offers 3.5% compound interest per year. Zara invests £9,000. How many complete years does it take for her investment to exceed £11,000?[5 marks]
  25. 25. A price falls by 15% each year. Starting from £8,000, find the value after 4 years and calculate the overall percentage decrease.[5 marks]

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Worked Answers

  1. 1. 72 ÷ 0.80 = £90
  2. 2. Profit = £72. 72 ÷ 360 × 100 = 20%
  3. 3. 34,500 ÷ 1.15 = £30,000
  4. 4. 504 ÷ 1.20 = £420
  5. 5. 324,000 ÷ 1.08 = £300,000
  6. 6. 6,000 × 1.04³ = 6,000 × 1.124864 = £6,749.18
  7. 7. Decrease = 192. 192 ÷ 1,200 × 100 = 16%
  8. 8. 84 × 1.125 = £94.50
  9. 9. 270 ÷ 0.60 = £450
  10. 10. 22,000 × 0.82 = £18,040; £18,040 × 0.82 = £14,792.80
  11. 11. 400 × 1.15 × 0.90 = 400 × 1.035 = £414. Overall change: 3.5% increase.
  12. 12. 3,200 ÷ 0.40 = 8,000
  13. 13. 8,000 × 1.05 = £8,400 (year 1); × 1.05 = £8,820 (year 2); × 1.05 = £9,261 (year 3). After year 3 it exceeds £9,000. Answer: 3 years.
  14. 14. 97.50 ÷ 0.65 = £150
  15. 15. Increase = £0.48m. 0.48 ÷ 2.4 × 100 = 20%
  16. 16. 4,800 × 0.625 = 3,000 kg
  17. 17. Profit = £37,000. 37,000 ÷ 185,000 × 100 = 20%
  18. 18. 800 × 1.25 × 1.20 = 800 × 1.50 = £1,200. Overall increase: 50%.
  19. 19. 14.80 × 1.075 = £15.91
  20. 20. Increase = 51,000. 51,000 ÷ 340,000 × 100 = 15%
  21. 21. 12,000 × r² = 14,520; r² = 1.21; r = 1.10. Annual rate = 10%.
  22. 22. Pre-VAT price = 108 ÷ 1.20 = £90. VAT = £108 − £90 = £18.
  23. 23. 1.10 × 0.90 = 0.99. The price is 1% lower than the original. The student is incorrect.
  24. 24. After 5 years: 9,000 × 1.035&sup5; = £10,689.17 < £11,000. After 6 years: 9,000 × 1.035&sup6; = £11,063.30 > £11,000. Answer: 6 years.
  25. 25. 8,000 × 0.85&sup4; = 8,000 × 0.52200625 = £4,176.05. Overall decrease: (8,000 − 4,176.05) ÷ 8,000 × 100 = 47.8%.

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