Year 8 Percentage Worksheet
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Year 8 Percentage Worksheet
Year 8 | Ages 12–13 | KS3
Answer all questions. Show full working including the method used.
Answer all questions. Show full working including the method used.
60 questions · 104 marks
Set 1 (Questions 1–20): Starter — percentage of amounts, increase and decrease
What is 35% of 240?
What is 12.5% of 160?
Increase £320 by 15% using the multiplier method.
Decrease 500 by 24% using the multiplier method.
What is 7% of 850?
Increase 960 by 12.5% using the multiplier method.
Decrease £740 by 35% using the multiplier method.
What is 22.5% of 400?
Write the multiplier for a 17% increase.
Write the multiplier for a 6.5% decrease.
Increase £1,200 by 8% using the multiplier method.
Decrease 2,500 by 16% using the multiplier method.
Express 45 as a percentage of 180.
Express £18 as a percentage of £72.
Express 63 as a percentage of 280.
A value rises from 200 to 250. Calculate the percentage increase.
A value falls from 320 to 272. Calculate the percentage decrease.
What is 3.5% of 2,000?
Increase £88 by 25% using the multiplier method.
Decrease 720 by 37.5% using the multiplier method.
Set 2 (Questions 21–40): Main — percentage change and reverse percentages
A coat costs £68 after a 15% discount. What was the original price?
A TV costs £720 after a 20% reduction. What was the original price?
A price of £85 includes VAT at 20%. What is the price before VAT?
After a 25% increase, a salary is £30,000. What was the original salary?
A value rises from £180 to £207. Calculate the percentage increase.
A jacket is in a 40% off sale. The sale price is £54. What was the original price?
After a 30% decrease, a value is 280. What was the original value?
A mobile phone costs £480. It is reduced by 12.5%. What is the sale price?
A value falls from £350 to £266. Calculate the percentage decrease.
After a 40% increase, a number is 1,120. What was the original number?
A laptop costs £612 after an 8% discount. What was the original price?
A salary of £26,400 is 10% more than last year. What was last year's salary?
A value rises from 480 to 576. Calculate the percentage increase.
After a 15% rise, a price is £126.50. What was the original price?
A ticket costs £34 after a 15% discount. What was the original price?
Express 78p as a percentage of £5.20.
A value falls from 1,440 to 1,008. Calculate the percentage decrease.
After a 60% increase, a value is 640. What was the original value?
A house was valued at £195,000 after a 5% rise. What was its previous value?
A value falls from 960 to 720. Calculate the percentage decrease.
Set 3 (Questions 41–60): Challenge — complex reverse percentages, compound change and reasoning
A car loses 18% of its value each year. It is worth £16,400 now. What was it worth one year ago?
A price is increased by 20% and then decreased by 20%. Starting from £250, what is the final price?
After two successive 10% increases, a value is 242. What was the original value?
A shop increases prices by 15%, then offers a 10% discount on the increased prices. Starting from £80, what is the final price?
A car bought for £14,000 depreciated by 12% per year for two years. What is it worth after two years?
A jacket is discounted by 25% and then a further 10% is taken off the discounted price. What single percentage discount is equivalent to these two discounts?
An investment of £3,200 grows by 5% per year for two years. What is it worth after two years?
After a 35% reduction followed by a 20% reduction off the new price, a TV costs £312. What was the original price?
A price rises by 8%, giving a new price of £216. The price then falls by 10%. What is the final price?
A school's roll increases by 4% each year. It currently has 1,352 pupils. How many did it have two years ago?
Express £1.26 as a percentage of £4.50, then increase £4.50 by that percentage.
A suit costs £374 after VAT is added at 20%. What is the pre-VAT price?
Two shops sell the same jacket. Shop A: was £95, now 30% off. Shop B: was £115, now 40% off. Which shop is cheaper, and by how much?
After a 12% pay rise, a worker earns £29,120. What did they earn before the rise?
A value is increased by 5%, then the result is decreased by 4%. Starting from 1,000, what is the final value?
Reasoning: A price is reduced by 20%. Then it is increased by 25% of the reduced price. Connor says the price is now the same as the original. Is he correct? Show working with a starting price of £100.
Reasoning: Two workers both receive a 5% pay rise. Worker A earns £20,000 and worker B earns £35,000. Explain why the percentage increase is the same but the cash increase is different. Calculate both cash increases.
Reasoning: After a 15% discount a coat costs £68. Freya works out the original price as £68 × 1.15 = £78.20. Explain her mistake and find the correct original price.
Reasoning: A car depreciates by 10% in year 1 and by 15% in year 2. A motorbike depreciates by 25% over the same two years. Starting from £10,000 each, which is worth more after two years? Show full calculations.
Reasoning: A shop claims "We have reduced all prices by 20% and then a further 20%." A customer says that is a total reduction of 40%. Who is correct? Use £100 to explain.
Free to print and use in your classroom. percentages.co.uk
Answer Sheet — Year 8 Percentage Worksheet (Set A)
Answers are shown below. When printed, the answer sheet always starts on a new page.
| Q | Answer | Marks |
|---|---|---|
| 1 | 84 | 1 |
| 2 | 20 | 1 |
| 3 | £368 | 1 |
| 4 | 380 | 1 |
| 5 | 59.50 | 1 |
| 6 | 1,080 | 1 |
| 7 | £481 | 1 |
| 8 | 90 | 1 |
| 9 | 1.17 | 1 |
| 10 | 0.935 | 1 |
| 11 | £1,296 | 1 |
| 12 | 2,100 | 1 |
| 13 | 25% | 1 |
| 14 | 25% | 1 |
| 15 | 22.5% | 1 |
| 16 | 25% | 1 |
| 17 | 15% | 1 |
| 18 | 70 | 1 |
| 19 | £110 | 1 |
| 20 | 450 | 1 |
| 21 | £80 | 2 |
| 22 | £900 | 2 |
| 23 | £70.83 | 2 |
| 24 | £24,000 | 2 |
| 25 | 15% | 1 |
| 26 | £90 | 2 |
| 27 | 400 | 2 |
| 28 | £420 | 2 |
| 29 | 24% | 1 |
| 30 | 800 | 2 |
| Q | Answer | Marks |
|---|---|---|
| 31 | £665.22 | 2 |
| 32 | £24,000 | 2 |
| 33 | 20% | 1 |
| 34 | £110 | 2 |
| 35 | £40 | 2 |
| 36 | 15% | 2 |
| 37 | 30% | 1 |
| 38 | 400 | 2 |
| 39 | £185,714.29 | 2 |
| 40 | 25% | 2 |
| 41 | £20,000 | 2 |
| 42 | £240 | 3 |
| 43 | 200 | 2 |
| 44 | £82.80 | 3 |
| 45 | £10,822.40 | 2 |
| 46 | 32.5% | 3 |
| 47 | £3,528 | 2 |
| 48 | £600 | 2 |
| 49 | £194.40 (original: £200; after 8% rise: £216; after 10% fall: £194.40) | 3 |
| 50 | 1,250 | 2 |
| 51 | £1.26 ÷ £4.50 × 100 = 28%. £4.50 × 1.28 = £5.76 | 3 |
| 52 | £311.67 | 2 |
| 53 | Shop A: £66.50. Shop B: £69. Shop A is cheaper by £2.50. | 3 |
| 54 | £26,000 | 2 |
| 55 | 1,008 | 2 |
| 56 | £100 × 0.8 = £80. £80 × 1.25 = £100. Connor is correct for this pair of percentage changes. | 2 |
| 57 | Worker A cash rise: £1,000. Worker B cash rise: £1,750. The same percentage of a larger base amount gives a larger cash value. | 3 |
| 58 | Freya incorrectly added 15% to the sale price. To reverse a 15% discount divide by 0.85: £68 ÷ 0.85 = £80. | 2 |
| 59 | Car: £10,000 × 0.9 × 0.85 = £7,650. Motorbike: £10,000 × 0.75 = £7,500. The car is worth more after two years. | 3 |
| 60 | £100 × 0.8 = £80. £80 × 0.8 = £64. Total reduction = 36%, not 40%. The customer is incorrect; the actual reduction is 36%. | 2 |
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