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Reverse Percentage Worksheet

KS3-GCSE | Years 8-11Intermediate to Higher25 questions

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

Worked Example 1 (after an increase)

After a 20% increase, a price is £360. Find the original price.

The new price represents 120% of the original, so: 1.20 × original = £360

Original = £360 ÷ 1.20 = £300

Worked Example 2 (after a decrease)

After a 15% reduction, a price is £340. Find the original price.

The new price represents 85% of the original, so: 0.85 × original = £340

Original = £340 ÷ 0.85 = £400

Find the original value in each question. Show your working. Give monetary answers in pounds.

Section A: After an increase

  1. 1. After a 10% increase, a price is £220. Find the original price.

  2. 2. After a 20% increase, a price is £480. Find the original price.

  3. 3. After a 25% increase, a value is 625. Find the original value.

  4. 4. After a 5% increase, a price is £315. Find the original price.

  5. 5. After a 15% pay rise, a salary is £34,500. Find the original salary.

  6. 6. After a 30% increase, a value is 1,170. Find the original value.

  7. 7. After a 12% increase, a price is £672. Find the original price.

  8. 8. After a 7.5% increase, a salary is £32,250. Find the original salary.

  9. 9. After a 35% increase, a value is £810. Find the original value.

  10. 10. After a 4% increase, a price is £520. Find the original price.

  11. 11. After a 22% increase, a price is £488. Find the original price.

  12. 12. After a 12.5% increase, a salary is £36,000. Find the original salary.

Section B: After a decrease

  1. 13. After a 10% reduction, a price is £162. Find the original price.

  2. 14. After a 20% reduction, a price is £320. Find the original price.

  3. 15. After a 25% discount, a price is £225. Find the original price.

  4. 16. After a 15% reduction, a price is £425. Find the original price.

  5. 17. After a 30% discount, a price is £420. Find the original price.

  6. 18. After a 5% discount, a price is £57. Find the original price.

  7. 19. After a 40% discount, a price is £180. Find the original price.

  8. 20. After a 12% reduction, a price is £440. Find the original price.

  9. 21. A quantity decreases by 35% to become 325. Find the original quantity.

  10. 22. After a 17.5% reduction, a price is £330. Find the original price.

Section C: Mixed and multi-step

  1. 23. A restaurant bill is £46 including a 15% service charge. What was the bill before the service charge was added?

  2. 24. A price is increased by 20% and then decreased by 10%. The final price is £432. Find the original price.

  3. 25. After VAT at 20% is added, an item costs £84. What was the pre-VAT price? A student says “subtract 20% from £84 to get £67.20”. Explain why this is wrong and give the correct answer.

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Worked Answers

Section A: After an increase

  1. 1. Original price = £200

    After a 10% increase, the new price is 110% of the original. Original = £220 ÷ 1.10 = £200

  2. 2. Original price = £400

    After a 20% increase, the new price is 120% of the original. Original = £480 ÷ 1.20 = £400

  3. 3. Original value = 500

    After a 25% increase, the new value is 125% of the original. Original = 625 ÷ 1.25 = 500

  4. 4. Original price = £300

    After a 5% increase, the new price is 105% of the original. Original = £315 ÷ 1.05 = £300

  5. 5. Original salary = £30,000

    After a 15% rise, the new salary is 115% of the original. Original = £34,500 ÷ 1.15 = £30,000

  6. 6. Original value = 900

    After a 30% increase, the new value is 130% of the original. Original = 1,170 ÷ 1.30 = 900

  7. 7. Original price = £600

    After a 12% increase, the new price is 112% of the original. Original = £672 ÷ 1.12 = £600

  8. 8. Original salary = £30,000

    After a 7.5% increase, the new salary is 107.5% of the original. Original = £32,250 ÷ 1.075 = £30,000

  9. 9. Original value = £600

    After a 35% increase, the new value is 135% of the original. Original = £810 ÷ 1.35 = £600

  10. 10. Original price = £500

    After a 4% increase, the new price is 104% of the original. Original = £520 ÷ 1.04 = £500

  11. 11. Original price = £400

    After a 22% increase, the new price is 122% of the original. Original = £488 ÷ 1.22 = £400

  12. 12. Original salary = £32,000

    After a 12.5% increase, the new salary is 112.5% of the original. Original = £36,000 ÷ 1.125 = £32,000

Section B: After a decrease

  1. 13. Original price = £180

    After a 10% reduction, the new price is 90% of the original. Original = £162 ÷ 0.90 = £180

  2. 14. Original price = £400

    After a 20% reduction, the new price is 80% of the original. Original = £320 ÷ 0.80 = £400

  3. 15. Original price = £300

    After a 25% discount, the new price is 75% of the original. Original = £225 ÷ 0.75 = £300

  4. 16. Original price = £500

    After a 15% reduction, the new price is 85% of the original. Original = £425 ÷ 0.85 = £500

  5. 17. Original price = £600

    After a 30% discount, the new price is 70% of the original. Original = £420 ÷ 0.70 = £600

  6. 18. Original price = £60

    After a 5% discount, the new price is 95% of the original. Original = £57 ÷ 0.95 = £60

  7. 19. Original price = £300

    After a 40% discount, the new price is 60% of the original. Original = £180 ÷ 0.60 = £300

  8. 20. Original price = £500

    After a 12% reduction, the new price is 88% of the original. Original = £440 ÷ 0.88 = £500

  9. 21. Original quantity = 500

    After a 35% decrease, the quantity is 65% of the original. Original = 325 ÷ 0.65 = 500

  10. 22. Original price = £400

    After a 17.5% reduction, the new price is 82.5% of the original. Original = £330 ÷ 0.825 = £400

Section C: Mixed and multi-step

  1. 23. Bill before service charge = £40

    The total including 15% service charge is 115% of the original bill. Original = £46 ÷ 1.15 = £40

  2. 24. Original price = £400

    Combined multiplier: 1.20 × 0.90 = 1.08. So the final price is 108% of the original. Original = £432 ÷ 1.08 = £400

  3. 25. Pre-VAT price = £70. The student's method is wrong.

    Correct working: £84 ÷ 1.20 = £70. The student subtracted 20% of £84 = £16.80, giving £67.20. This is wrong because the VAT is 20% of the original price (£70), not 20% of the final price (£84). VAT = 20% of £70 = £14, so £70 + £14 = £84. Subtracting a percentage from the final price does not reverse the percentage increase.

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