Percentages
Ratio, proportion and rates of change
- Crossover
- Non-calculator
- 8 questions
- 29 marks
Questions marked Higher are aimed at the Higher tier.
These are original practice questions, not a past paper. This site is independent and not affiliated with AQA or Pearson.
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Find $15\%$ of $80$.
2 marks
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Increase $60$ by $20\%$.
2 marks
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A shirt costs £$45$. It is reduced by $30\%$ in a sale. Find the sale price.
3 marks
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A price rises from £$40$ to £$50$. Find the percentage increase.
3 marks
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A television costs £$360$ after a $20\%$ reduction. Find the original price.
4 marks
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Sam earns £$24000$. The salary increases by $4\%$, then by a further $5\%$ of the new salary. Find the salary after both increases.
4 marks
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In a sale, prices are reduced by $15\%$, and a coat is then reduced by a further $10\%$ of the sale price. The final price is £$91.80$. Find the original price. Higher
5 marks
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A shop buys an item for £$80$ and sells it for £$110$. Find the percentage profit. The selling price is then reduced by $20\%$. Find the new percentage profit. What selling price gives a $25\%$ profit on the cost price? Higher
6 marks
Mark scheme
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Answer. $12$
- $10\% = 8$ and $5\% = 4$.
- $12$
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Answer. $72$
- $20\%$ of $60$ is $12$.
- $72$
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Answer. £$31.50$
- $30\%$ of £$45$ is £$13.50$.
- £$45 - £13.50 = £31.50$.
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Answer. $25\%$
- The increase is £$10$.
- $\dfrac{10}{40} \times 100 = 25\%$
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Answer. £$450$
- £$360$ is $80\%$ of the original price.
- $360 \div 0.8 = 450$
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Answer. £$26208$
- $24000 \times 1.04 = 24960$
- $24960 \times 1.05 = 26208$
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Answer. £$120$
- The combined multiplier is $0.85 \times 0.9 = 0.765$.
- $91.80 \div 0.765 = 120$
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Answer. $37.5\%$, then $10\%$, and a selling price of £$100$
- Profit £$30$ on £$80$ is $37.5\%$.
- Sale price $= 110 \times 0.8 = 88$, so the profit is £$8$, which is $10\%$.
- A $25\%$ profit means a selling price of $80 \times 1.25 = £100$.