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Percentage Word Problems Worksheet

KS3-GCSE | Years 7-11Mixed30 questions

Free to print and use in your classroom. No sign-up required.

Read each problem carefully. Show your working to gain full marks.

Section A: Straightforward (Questions 1-10)

  1. 1. A jacket costs £60. It is reduced by 20% in a sale. Find the sale price.

  2. 2. A class of 30 students sat a test. 24 passed. What percentage passed?

  3. 3. A shop adds VAT at 20% to a price of £35. What is the price with VAT included?

  4. 4. Tom earns £24,000 per year. He receives a 5% pay rise. What is his new salary?

  5. 5. 15% of a number is 45. What is the number?

  6. 6. A phone costs £480. It is discounted by 15%. Find the sale price.

  7. 7. A school has 900 pupils. 48% are boys. How many boys are there?

  8. 8. Sarah spends £36 on food from a budget of £120. What percentage of her budget does she spend on food?

  9. 9. A train ticket costs £55 before a 10% railcard discount. Find the discounted price.

  10. 10. A shop's daily sales are £2,400. If 15% is profit, how much profit is made?

Section B: Intermediate (Questions 11-20)

  1. 11. After a 30% increase, a price is £390. Find the original price.

  2. 12. A house was bought for £185,000 and sold for £222,000. Calculate the percentage profit.

  3. 13. An energy bill rises from £1,200 to £1,440 per year. Calculate the percentage increase.

  4. 14. A laptop costs £840 including VAT at 20%. Find the price before VAT.

  5. 15. Fatima scores 68 marks out of 80 in an exam. Her friend scores 85%. Who scores more? Show your working.

  6. 16. A salary of £28,000 increases by 3.5%. Find the new salary.

  7. 17. In a football season, a team wins 18 out of 30 games. What percentage of games do they win?

  8. 18. A recipe uses 350 g of butter. A reduced-fat version uses 30% less butter. How much butter does the reduced-fat version use?

  9. 19. A savings account pays 3% simple interest per year. Adam deposits £4,000. How much interest does he earn in 2 years?

  10. 20. After a 25% reduction, a sofa costs £675. What was the original price?

Section C: Challenging (Questions 21-30)

  1. 21. A car costs £14,500. It depreciates by 18% in year 1 and 12% in year 2. What is it worth after 2 years?

  2. 22. The price of a house increases by 8% in year 1, then decreases by 5% in year 2. Starting from £230,000, find the value after 2 years.

  3. 23. A packet of biscuits contains 40% fewer calories than the original. The original has 250 calories. How many calories does the new version have?

  4. 24. A worker earns £16.50 per hour. Her pay rises by 4%. What is her new hourly rate?

  5. 25. A gym has 540 members. 35% are women, 45% are men, and the rest are juniors. How many junior members are there?

  6. 26. An investment of £5,000 grows at 4% compound interest per year. A second investment of £4,500 grows at 6% compound interest per year. How much is each worth after 3 years?

  7. 27. In a survey, 240 people said they owned a dog. This was 40% of those surveyed. How many people were surveyed in total?

  8. 28. A shop buys a coat for £84 and sells it for £112. Calculate the percentage profit.

  9. 29. A train journey takes 2 hours and 30 minutes. Due to engineering works, it takes 15% longer. How long does the journey take? Give your answer in hours and minutes.

  10. 30. After 20% VAT is added to a price of £P, the total is £72. Find the value of P. Then find the amount of VAT charged.

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Worked Answers

Section A: Straightforward

  1. 1. 60 × 0.80 = £48
  2. 2. 24 ÷ 30 × 100 = 80%
  3. 3. 35 × 1.20 = £42
  4. 4. 24,000 × 1.05 = £25,200
  5. 5. 45 ÷ 0.15 = 300
  6. 6. 480 × 0.85 = £408
  7. 7. 900 × 0.48 = 432 boys
  8. 8. 36 ÷ 120 × 100 = 30%
  9. 9. 55 × 0.90 = £49.50
  10. 10. 2,400 × 0.15 = £360

Section B: Intermediate

  1. 11. 390 ÷ 1.30 = £300
  2. 12. Profit = £37,000. 37,000 ÷ 185,000 × 100 = 20%
  3. 13. Increase = £240. 240 ÷ 1,200 × 100 = 20%
  4. 14. 840 ÷ 1.20 = £700
  5. 15. Fatima: 68 ÷ 80 × 100 = 85%. Her friend also scores 85%. They score the same.
  6. 16. 28,000 × 1.035 = £28,980
  7. 17. 18 ÷ 30 × 100 = 60%
  8. 18. 350 × 0.70 = 245 g
  9. 19. 4,000 × 0.03 × 2 = £240
  10. 20. 675 ÷ 0.75 = £900

Section C: Challenging

  1. 21. 14,500 × 0.82 = £11,890; £11,890 × 0.88 = £10,463.20
  2. 22. 230,000 × 1.08 = £248,400; £248,400 × 0.95 = £235,980
  3. 23. 250 × 0.60 = 150 calories
  4. 24. 16.50 × 1.04 = £17.16
  5. 25. 100% − 35% − 45% = 20% are juniors. 540 × 0.20 = 108 juniors
  6. 26. First: 5,000 × 1.04³ = 5,000 × 1.124864 = £5,624.32. Second: 4,500 × 1.06³ = 4,500 × 1.191016 = £5,359.57.
  7. 27. 240 ÷ 0.40 = 600 people
  8. 28. Profit = £28. 28 ÷ 84 × 100 = 33.3% (to 1 d.p.)
  9. 29. 150 minutes × 1.15 = 172.5 minutes = 2 hours 52 minutes 30 seconds
  10. 30. P × 1.20 = 72; P = 72 ÷ 1.20 = £60. VAT charged = £72 − £60 = £12.

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