Year 10 Percentage Worksheet
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Year 10 Percentage Worksheet
Year 10 | Ages 14–15 | GCSE
Answer all questions. Show full working including the method used. Give answers to 2 decimal places where appropriate.
Answer all questions. Show full working including the method used. Give answers to 2 decimal places where appropriate.
60 questions · 130 marks
Set 1 (Questions 1–20): Starter — percentage of amounts, increase, decrease and expressing as a percentage
What is 35% of 420?
What is 15% of 680?
Increase £320 by 25%.
Decrease 540 by 30%.
Express 63 as a percentage of 180.
Express 84p as a percentage of £3.50.
Calculate 17.5% of £240.
Increase £450 by 12%.
Decrease £750 by 20%.
A value rises from 80 to 92. Calculate the percentage increase.
A value falls from 600 to 480. Calculate the percentage decrease.
Increase £180 by 35%.
Decrease £920 by 15%.
What is 45% of 360?
Express £14 as a percentage of £56.
A value rises from 250 to 300. Calculate the percentage increase.
Decrease 840 by 12.5%.
Calculate 8% of £1,250.
Increase £95 by 60%.
A value falls from 480 to 360. Calculate the percentage decrease.
Set 2 (Questions 21–40): Main — reverse percentages, percentage change and compound interest
After a 20% reduction, a coat costs £76. Find the original price.
After a 15% pay rise, a salary is £34,500. Find the original salary.
Calculate the compound interest earned on £2,000 at 3% per year for 2 years. Give your answer to the nearest penny.
A shop buys goods for £160 and sells them for £200. Calculate the percentage profit.
A bike is bought for £350 and sold for £280. Calculate the percentage loss.
After an 8% price increase, an item costs £270. Find the original price.
£1,500 is invested at 4% compound interest per year for 2 years. What is the total amount? Give your answer to the nearest penny.
After a 25% reduction, an item costs £135. Find the original price.
A value rises from 360 to 414. Calculate the percentage increase.
A car bought for £16,000 depreciates at 12% per year. Find its value after 2 years. Give your answer to the nearest penny.
After a 12% reduction, a price is £176. Find the original price.
£3,000 is invested at 5% compound interest per year for 2 years. How much interest is earned in total? Give your answer to the nearest penny.
A price is reduced by 10% and then by a further 20%. Find the total percentage reduction from the original price.
After a 7.5% pay rise, a wage is £32,250. Find the original wage.
A retailer buys items for £240 and sells them for £288. Calculate the percentage profit.
After a 30% increase, a price is £390. Find the original price.
£5,000 is invested at 2% compound interest per year for 2 years. What is the total amount? Give your answer to the nearest penny.
A television is bought for £1,200 and sold for £900. Calculate the percentage loss.
After a 35% reduction, an item costs £91. Find the original price.
£800 is invested at 6% compound interest per year for 2 years. What is the total amount? Give your answer to the nearest penny.
Set 3 (Questions 41–60): Challenge — multi-step compound problems and GCSE-style reasoning
£4,000 is invested at 4% compound interest per year for 3 years. Find the total value. Give your answer to the nearest penny.
A car bought for £18,000 depreciates at 15% per year. Find its value after 3 years. Give your answer to the nearest penny.
A price is increased by 20% and then decreased by 20%. Starting from £500, find the final price and the overall percentage change.
£2,500 is invested at 3.5% compound interest per year for 3 years. Find the total value. Give your answer to the nearest penny.
After 2 years of compound growth at 5% per year, an investment is worth £2,205. Find the original amount invested.
A laptop costs £1,200. In year 1 it loses 25% of its value, in year 2 it loses 20% and in year 3 it loses 15%. Find its value after 3 years.
£3,500 is invested at 2.5% compound interest per year for 4 years. Find the total value. Give your answer to the nearest penny.
A house worth £200,000 rises in value by 6% in year 1 and then falls by 4% in year 2. Find its value at the end of year 2.
After 3 years of compound growth at 5% per year, an investment is worth £5,788.13. Find the original amount invested.
A car bought for £22,000 depreciates at 18% per year for 3 years. Find its value after 3 years. Give your answer to the nearest penny.
£4,500 is invested at 3.5% compound interest per year for 3 years. Find the total value. Give your answer to the nearest penny.
A price is reduced by 15% and then increased by 10%. Starting from £400, find the final price and the overall percentage change.
£3,000 is invested at 4.5% compound interest per year. How many complete years does it take for the investment to exceed £3,600? Show year-by-year working.
A retailer buys goods for £320, marks the price up by 40%, and then offers a 15% discount. Find the final selling price and the actual percentage profit on the cost price.
A car bought for £25,000 depreciates by 20% in year 1, by 15% in year 2 and by 10% in year 3. Find its value after 3 years and the overall percentage decrease in value.
Reasoning: A price rises by 10% and then falls by 10%. Explain why the final price is not the same as the original, and calculate the overall percentage change.
Reasoning: Bank A pays 3% compound interest per year for 4 years. Bank B pays 12% simple interest over 4 years. Ravi invests £2,000 in each. Show which bank gives a greater total return and find the difference to the nearest penny.
Reasoning: A salesman claims: "I cut the price by 30% and then gave a further 20% off, so the total discount is 50%." Explain why he is wrong and find the actual total percentage reduction.
Reasoning: A car is bought for £12,000 and depreciates at 20% per year. Its owner claims it will be worth nothing after 5 years because 20% × 5 = 100%. Explain the error and find the actual value after 5 years.
Reasoning: Ahmed says that if a quantity falls by 50% and then rises by 50%, it returns to its original value. Show he is wrong using £200 as a starting value, and state the overall percentage change.
Free to print and use in your classroom. percentages.co.uk
Answer Sheet — Year 10 Percentage Worksheet (Set A)
Answers are shown below. When printed, the answer sheet always starts on a new page.
| Q | Answer | Marks |
|---|---|---|
| 1 | 147 | 1 |
| 2 | 102 | 1 |
| 3 | £400 | 1 |
| 4 | 378 | 1 |
| 5 | 35% | 1 |
| 6 | 24% | 1 |
| 7 | £42 | 1 |
| 8 | £504 | 1 |
| 9 | £600 | 1 |
| 10 | 15% | 1 |
| 11 | 20% | 1 |
| 12 | £243 | 1 |
| 13 | £782 | 1 |
| 14 | 162 | 1 |
| 15 | 25% | 1 |
| 16 | 20% | 1 |
| 17 | 735 | 1 |
| 18 | £100 | 1 |
| 19 | £152 | 1 |
| 20 | 25% | 1 |
| 21 | £95 | 2 |
| 22 | £30,000 | 2 |
| 23 | Interest: £121.80; total: £2,121.80 | 3 |
| 24 | 25% | 2 |
| 25 | 20% | 2 |
| 26 | £250 | 2 |
| 27 | £1,622.40 | 2 |
| 28 | £180 | 2 |
| 29 | 15% | 2 |
| 30 | £12,390.40 | 3 |
| Q | Answer | Marks |
|---|---|---|
| 31 | £200 | 2 |
| 32 | Interest: £307.50; total: £3,307.50 | 3 |
| 33 | 28% | 2 |
| 34 | £30,000 | 2 |
| 35 | 20% | 2 |
| 36 | £300 | 2 |
| 37 | £5,202 | 2 |
| 38 | 25% | 2 |
| 39 | £140 | 2 |
| 40 | £898.88 | 3 |
| 41 | £4,499.46 | 3 |
| 42 | £11,054.25 | 3 |
| 43 | £480; overall decrease of 4% | 3 |
| 44 | £2,771.79 | 3 |
| 45 | £2,000 | 3 |
| 46 | £612 | 3 |
| 47 | £3,863.35 | 3 |
| 48 | £203,520 | 4 |
| 49 | £5,000 | 3 |
| 50 | £12,130.10 | 4 |
| 51 | £4,989.23 | 3 |
| 52 | £374; overall decrease of 6.5% | 4 |
| 53 | 5 years (after 4 years: £3,577.56; after 5 years: £3,738.55) | 4 |
| 54 | Selling price: £380.80; percentage profit: 19% | 4 |
| 55 | Value: £15,300; overall decrease: 38.8% | 4 |
| 56 | The 10% decrease applies to the already-increased price. Multiplier: 1.10 × 0.90 = 0.99; overall decrease of 1%. Example: 100 × 1.10 = 110; 110 × 0.90 = 99. | 3 |
| 57 | Bank A: £2,000 × 1.03⁴ = £2,251.02. Bank B: £2,000 + (£2,000 × 0.12) = £2,240. Bank A gives more interest. Difference: £11.02. | 3 |
| 58 | The second 20% is applied to the already-reduced price. Combined multiplier: 0.70 × 0.80 = 0.56; total reduction = 44%, not 50%. | 3 |
| 59 | Each year 20% of the current value is lost, not 20% of the original. £12,000 × 0.80⁵ = £12,000 × 0.32768 = £3,932.16. The value falls but never reaches zero. | 3 |
| 60 | £200 × 0.50 = £100; £100 × 1.50 = £150. Final value: £150, not £200. Multiplier: 0.50 × 1.50 = 0.75; overall decrease of 25%. | 3 |
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