Percentage Homework Sheet - GCSE
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Percentage Homework Sheet - GCSE
Answer all 15 questions. Show all working. Marks are shown in brackets for each question.
Calculate 23% of 840.
[1 mark]Increase £560 by 14%.
[1 mark]Decrease £1,200 by 17.5%.
[1 mark]A laptop is bought for £650 and sold for £507. Calculate the percentage loss.
[2 marks]A jacket costs £84 including VAT at 20%. Calculate the price of the jacket before VAT.
[2 marks]After a 12% pay rise, Priya earns £3,024 per month. What was her monthly salary before the pay rise?
[2 marks]A television is reduced by 35% in a sale. The sale price is £292.50. What was the original price?
[2 marks]Express £34 profit on a cost price of £136 as a percentage profit.
[1 mark]A car was bought for £15,000. In the first year it depreciated by 18% and in the second year by 12%. What was the value of the car after two years?
[3 marks]A house price increases by 6% per year for 4 years. If the house is worth £220,000 now, what will it be worth in 4 years? Give your answer to the nearest pound.
[3 marks]Nina invests £4,500 at a compound interest rate of 2.5% per year. How much interest does she earn in total after 3 years? Give your answer to the nearest penny.
[3 marks]A shop buys phones for £180 each and sells them for £261. Calculate the percentage profit.
[2 marks]An item is sold for £345 after a 15% increase. What was the original price?
[2 marks]Sam's electricity bill is £95 per month. It rises by 8% in April and then by a further 5% in October. What is Sam's monthly bill after both increases? Give your answer to the nearest penny.
[3 marks]A population of bacteria doubles in size and then decreases by 40%. Express the overall change as a percentage increase or decrease from the original population.
[3 marks]
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Worked Answers
- Q1: 0.23 × 840 = 193.2
- Q2: £560 × 1.14 = £638.40
- Q3: £1,200 × 0.825 = £990
- Q4: Loss = £650 − £507 = £143. Percentage loss = (143 ÷ 650) × 100 = 22%
- Q5: £84 represents 120%. Original price = £84 ÷ 1.20 = £70
- Q6: £3,024 represents 112%. Original = £3,024 ÷ 1.12 = £2,700
- Q7: £292.50 represents 65%. Original price = £292.50 ÷ 0.65 = £450
- Q8: (34 ÷ 136) × 100 = 25%
- Q9: After year 1: £15,000 × 0.82 = £12,300. After year 2: £12,300 × 0.88 = £10,824
- Q10: £220,000 × 1.06&sup4; = £220,000 × 1.26247696 = £277,745
- Q11: Amount after 3 years: £4,500 × 1.025³ = £4,500 × 1.076890625 = £4,845.91. Interest earned = £4,845.91 − £4,500 = £345.91
- Q12: Profit = £261 − £180 = £81. Percentage profit = (81 ÷ 180) × 100 = 45%
- Q13: £345 represents 115%. Original = £345 ÷ 1.15 = £300
- Q14: After April: £95 × 1.08 = £102.60. After October: £102.60 × 1.05 = £107.73
- Q15: Start with 100. After doubling: 200. After 40% decrease: 200 × 0.60 = 120. Overall change = 20 units increase on 100. 20% overall increase.
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