Year 9 Percentage Worksheet
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Year 9 Percentage Worksheet
Year 9 | Ages 13–14 | KS3/GCSE
Answer all questions. Show full method. Give answers to 2 decimal places where appropriate.
Answer all questions. Show full method. Give answers to 2 decimal places where appropriate.
60 questions · 107 marks
Set 1 (Questions 1–20): Starter — percentage of amounts, increase, decrease and basic reverse
What is 18% of 350?
What is 37.5% of 480?
Increase £620 by 15% using the multiplier method.
Decrease 840 by 22.5% using the multiplier method.
After a 20% increase, a price is £240. What was the original price?
After a 25% decrease, a value is 330. What was the original value?
After a 10% increase, a salary is £30,800. What was the original salary?
A TV costs £612 after a 10% discount. What was the original price?
A value rises from £360 to £414. Calculate the percentage increase.
A value falls from 2,400 to 1,680. Calculate the percentage decrease.
Express 84p as a percentage of £4.80.
After a 40% reduction, a coat costs £78. What was the original price?
Increase 2,400 by 7.5% using the multiplier method.
What is 6.5% of 1,200?
After a 35% discount, a bag costs £58.50. What was the original price?
A value rises from 560 to 700. Calculate the percentage increase.
Decrease £1,640 by 12.5% using the multiplier method.
After a 15% increase, a rent is £920. What was the original rent?
Express 91 as a percentage of 350.
After a 30% decrease, a price is £175. What was the original price?
Set 2 (Questions 21–40): Main — reverse percentages and percentage change
After a 7.5% rise, a salary is £32,250. What was the original salary?
A price of £141 includes VAT at 17.5%. What is the price before VAT?
A value rises from £540 to £594. Calculate the percentage increase.
A jacket sells for £119, which includes a 40% profit on the cost price. What was the cost price?
After a 12% discount, a price is £352. What was the original price?
A value falls from 640 to 448. Calculate the percentage decrease.
After a 60% increase, a value is 2,080. What was the original value?
A price is reduced by 25% and then by a further 20% off the reduced price. What single percentage discount is this equivalent to?
After a 35% rise, a price is £675. What was the original price?
A value rises from 360 to 414. Calculate the percentage increase.
A house is worth £252,000 after a 5% increase. What was it worth before the increase?
A car was bought for £22,000 and sold for £16,500. Calculate the percentage loss.
A town's population falls from 48,000 to 39,600. Calculate the percentage decrease.
After a 4% pay rise, a salary is £26,000. What was the original salary?
A quantity falls by 60% to become 800. What was the original quantity?
A value increases by 20% and then decreases by 20%. Starting from 500, what is the final value?
Express £3.78 as a percentage of £18.
After a 15% reduction followed by a 10% reduction off the new price, a price is £306. What was the original price?
A shop increases prices by 8%, then offers a 5% discount. Starting from £200, what is the final price?
A jacket originally costs £180 and is sold for £135. Calculate the percentage reduction.
Set 3 (Questions 41–60): Challenge — compound interest, depreciation and multi-step reasoning
£800 is invested at 5% compound interest per year for 2 years. What is the total amount?
£1,500 is invested at 4% compound interest per year for 3 years. What is it worth?
A car bought for £18,000 depreciates at 15% per year. What is it worth after 3 years? Give your answer to the nearest pound.
£2,000 is invested at 3.5% compound interest per year for 2 years. What is it worth?
A population of 25,000 grows at 2% per year. What is the population after 4 years? Give your answer to the nearest whole number.
£5,000 is invested at 2.5% compound interest per year for 3 years. What is it worth?
A house bought for £200,000 increases in value by 6% in year 1, 4% in year 2 and 3% in year 3. What is it worth after 3 years? Give your answer to the nearest pound.
A motorbike depreciates at 20% per year. It cost £4,500 new. What is it worth after 2 years?
Invest £3,600 at 3% compound interest for 4 years. How much interest is earned? Give your answer to the nearest penny.
A laptop depreciates at 25% per year. It cost £960 when new. What is it worth after 3 years?
Two banks offer savings rates. Bank A pays 4% compound interest per year. Bank B pays 4.1% simple interest per year. For £2,000 over 3 years, which bank pays more? Show your working.
A collectible toy increases in value by 8% per year. It is worth £540 now. What was it worth 2 years ago?
An investment of £10,000 grows at 5% compound interest per year. After how many whole years will it first exceed £12,000? Show your year-by-year working.
A van depreciates at 18% per year. It was bought for £24,000. What is it worth after 2 years? Give your answer to the nearest pound.
£6,000 is invested at 2% compound interest per year for 5 years. What is it worth? Give your answer to the nearest penny.
Reasoning: A price increases by 10% in year 1 and decreases by 10% in year 2. Starting from £500, show that the final price is not £500 and explain why.
Reasoning: £4,000 is invested at 3% compound interest per year. A different account offers 3% simple interest per year. After 5 years, which account has earned more interest? Show full calculations for both accounts.
Reasoning: A car loses 30% of its value in the first year and 20% of its remaining value in the second year. Liam says it has lost 50% of its original value over two years. Show whether he is correct.
Reasoning: Two investments both start at £5,000. Investment A grows at 6% compound interest per year. Investment B grows at 6% simple interest per year. After 3 years, what is the difference in their values? Explain which is better and why.
Reasoning: A house is worth £180,000. It increases in value by 5% per year for 3 years. The owner expects to earn £27,000 profit (based on 5% of £180,000 × 3 years). Show whether this expectation is correct and calculate the actual profit.
Free to print and use in your classroom. percentages.co.uk
Answer Sheet — Year 9 Percentage Worksheet (Set A)
Answers are shown below. When printed, the answer sheet always starts on a new page.
| Q | Answer | Marks |
|---|---|---|
| 1 | 63 | 1 |
| 2 | 180 | 1 |
| 3 | £713 | 1 |
| 4 | 651 | 1 |
| 5 | £200 | 1 |
| 6 | 440 | 1 |
| 7 | £28,000 | 1 |
| 8 | £680 | 1 |
| 9 | 15% | 1 |
| 10 | 30% | 1 |
| 11 | 17.5% | 1 |
| 12 | £130 | 1 |
| 13 | 2,580 | 1 |
| 14 | 78 | 1 |
| 15 | £90 | 1 |
| 16 | 25% | 1 |
| 17 | £1,435 | 1 |
| 18 | £800 | 1 |
| 19 | 26% | 1 |
| 20 | £250 | 1 |
| 21 | £30,000 | 2 |
| 22 | £120 | 2 |
| 23 | 10% | 2 |
| 24 | £85 | 2 |
| 25 | £400 | 2 |
| 26 | 30% | 1 |
| 27 | 1,300 | 2 |
| 28 | 40% | 2 |
| 29 | £500 | 2 |
| 30 | 15% | 1 |
| Q | Answer | Marks |
|---|---|---|
| 31 | £240,000 | 2 |
| 32 | 25% | 2 |
| 33 | 17.5% | 2 |
| 34 | £25,000 | 2 |
| 35 | 2,000 | 2 |
| 36 | 480 | 2 |
| 37 | 21% | 2 |
| 38 | £400 | 2 |
| 39 | £205.20 | 2 |
| 40 | 25% | 2 |
| 41 | £882 | 2 |
| 42 | £1,687.30 | 2 |
| 43 | £11,054 | 3 |
| 44 | £2,142.45 | 2 |
| 45 | 27,061 | 3 |
| 46 | £5,384.45 | 2 |
| 47 | £227,251 | 3 |
| 48 | £2,880 | 2 |
| 49 | Amount: £3,600 × 1.03⁴ = £4,051.47. Interest earned: £451.47. | 3 |
| 50 | £405 | 2 |
| 51 | Bank A: £2,000 × 1.04³ = £2,249.73. Bank B: £2,000 + (£2,000 × 0.041 × 3) = £2,246. Bank A pays more. | 3 |
| 52 | £463.11 | 2 |
| 53 | Year 1: £10,500. Year 2: £11,025. Year 3: £11,576.25. Year 4: £12,155.06. First exceeds £12,000 after 4 years. | 3 |
| 54 | £16,166 | 2 |
| 55 | £6,624.32 | 2 |
| 56 | £500 × 1.1 = £550. £550 × 0.9 = £495. The final price is £495, not £500. The 10% decrease is applied to the larger increased value, so the decrease in pounds is larger than the original increase. | 2 |
| 57 | Compound: £4,000 × 1.03⁵ = £4,637.09. Interest: £637.09. Simple: £4,000 × 0.03 × 5 = £600. The compound account earns more interest (by £37.09). | 3 |
| 58 | £100 × 0.7 = £70. £70 × 0.8 = £56. Total loss = 44%, not 50%. Liam is incorrect. | 2 |
| 59 | Investment A: £5,000 × 1.06³ = £5,955.08. Investment B: £5,000 + (£5,000 × 0.06 × 3) = £5,900. Difference: £55.08. Investment A (compound) is better because each year interest is earned on previous years' accumulated interest, not just the principal. | 3 |
| 60 | £180,000 × 1.05³ = £208,327.50. Actual profit: £28,327.50. Simple expectation: £27,000. The actual profit is higher because each year the percentage applies to a growing value. | 3 |
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