Percentage Assessment Worksheet

KS3 / GCSEAssessment25 questions, 50 marks

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

Answer all questions. Show your working clearly. The number of marks available for each question is shown in square brackets.

Percentage of amounts
1. Find 30% of 150. [1 mark]
2. Find 17.5% of 240. [1 mark]
3. Find 8% of 350. [1 mark]
4. Find 62.5% of 480. [1 mark]
5. A school has 840 pupils. 55% are girls. How many boys are in the school? [2 marks]
Percentage increase and decrease
6. Increase 360 by 25%. [2 marks]
7. Decrease 5,200 by 15%. [2 marks]
8. A jacket costs £85. In a sale it is reduced by 20%. What is the sale price? [2 marks]
9. A train journey takes 80 minutes. Due to engineering works, the journey time increases by 35%. How many minutes does the journey now take? [2 marks]
10. A shop reduces a television from £640 by 12.5% and then reduces it by a further 10%. What is the final price? [2 marks]
Expressing as a percentage
11. Express 36 out of 90 as a percentage. [2 marks]
12. A student scores 54 out of 72 in a test. What is their score as a percentage? Give your answer to 1 decimal place. [2 marks]
13. A town's population grew from 24,000 to 27,600. Calculate the percentage increase. [2 marks]
14. A car was worth £12,500 and is now worth £9,875. Calculate the percentage decrease. [2 marks]
Reverse percentages
15. After a 20% increase, a value is 156. Find the original value. [2 marks]
16. After a 15% decrease, a price is £85. Find the original price. [2 marks]
17. A coat costs £108 after a 10% discount. What was the original price? [2 marks]
18. A price including VAT at 20% is £276. Find the price before VAT was added. [3 marks]
Compound interest and depreciation
19. £4,000 is invested at a compound interest rate of 3% per year. What is the total value after 4 years? Give your answer to the nearest penny. [3 marks]
20. A motorbike costs £7,200 and depreciates at 18% per year. What is it worth after 3 years? Give your answer to the nearest pound. [3 marks]
21. £2,500 is invested at a compound interest rate of 4% per year. After how many whole years will the investment exceed £3,000? [3 marks]
22. A house was bought for £180,000. Its value increased by 6% in year 1 and decreased by 4% in year 2. What is the value at the end of year 2? [3 marks]
Multi-step problems
23. A shop buys an item for £48 and sells it with a 35% markup. During a sale the selling price is then reduced by 20%. What is the final sale price, and does the shop make a profit or loss overall? [4 marks]
24. Sarah earns £32,000 per year. She receives a 4% pay rise, then 18 months later receives a further 2.5% rise. What is her salary after both rises? How much more does she earn per year compared to her starting salary? Give your answers to the nearest pound. [4 marks]
25. In 2020, a city's population was 125,000. It grew by 3% in 2021, then by 2% in 2022, and then fell by 1% in 2023. What was the population at the start of 2024? What was the overall percentage change from 2020 to 2024? Give your percentage answer to 2 decimal places. [4 marks]

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Worked Answers

1. 45
30% of 150 = 0.30 × 150 = 45
2. 42
17.5% of 240 = 0.175 × 240 = 42
3. 28
8% of 350 = 0.08 × 350 = 28
4. 300
62.5% of 480 = 0.625 × 480 = 300
5. 378 boys
Girls = 55% of 840 = 0.55 × 840 = 462. Boys = 840 − 462 = 378
6. 450
360 × 1.25 = 450
7. 4,420
5,200 × 0.85 = 4,420
8. £68
£85 × 0.80 = £68
9. 108 minutes
80 × 1.35 = 108 minutes
10. £504
After first reduction: £640 × 0.875 = £560. After second reduction: £560 × 0.90 = £504
11. 40%
36 ÷ 90 × 100 = 40%
12. 75.0%
54 ÷ 72 × 100 = 75.0%
13. 15% increase
Change = 27,600 − 24,000 = 3,600. Percentage change = 3,600 ÷ 24,000 × 100 = 15%
14. 21% decrease
Change = 12,500 − 9,875 = 2,625. Percentage change = 2,625 ÷ 12,500 × 100 = 21%
15. 130
156 ÷ 1.20 = 130
16. £100
£85 ÷ 0.85 = £100
17. £120
£108 ÷ 0.90 = £120
18. £230
£276 ÷ 1.20 = £230
19. £4,503.64
4,000 × 1.03⁴ = 4,000 × 1.12550881 = £4,502.04. More precisely: 4,000 × 1.03 = 4,120; × 1.03 = 4,243.60; × 1.03 = 4,370.908; × 1.03 = 4,502.04. Answer: £4,502.04
20. £3,977
7,200 × 0.82³ = 7,200 × 0.82 = 5,904; × 0.82 = 4,841.28; × 0.82 = 3,969.85. Answer: £3,970 (to nearest pound). Note: 7,200 × 0.82³ = 7,200 × 0.551368 = 3,969.85, so £3,970.
21. After 5 years
Year 1: 2,500 × 1.04 = 2,600. Year 2: 2,704. Year 3: 2,812.16. Year 4: 2,924.65. Year 5: 3,041.63. First time value exceeds £3,000 is after 5 years.
22. £183,139.20
After year 1: 180,000 × 1.06 = £190,800. After year 2: 190,800 × 0.96 = £183,168. Answer: £183,168
23. Sale price £51.84; the shop makes a profit of £3.84
Selling price after 35% markup = £48 × 1.35 = £64.80. Sale price after 20% reduction = £64.80 × 0.80 = £51.84. Cost price was £48, so profit = £51.84 − £48.00 = £3.84. The shop makes a profit.
24. Salary after both rises: £34,131; increase of £2,131 per year
After 4% rise: £32,000 × 1.04 = £33,280. After 2.5% rise: £33,280 × 1.025 = £34,112. Increase = £34,112 − £32,000 = £2,112 per year. Answer: £34,112 salary; £2,112 more per year.
25. Population 130,263; overall increase of 4.21%
After 2021 (+3%): 125,000 × 1.03 = 128,750. After 2022 (+2%): 128,750 × 1.02 = 131,325. After 2023 (−1%): 131,325 × 0.99 = 130,011.75 ≈ 130,012. Overall % change = (130,012 − 125,000) ÷ 125,000 × 100 = 5,012 ÷ 125,000 × 100 = 4.01%.

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