AQA · Mathematics · 8300
GCSE Maths: Percentages: reverse
Ratio & Proportion · AQA GCSE Maths (8300). Cards are generated from the Corbettmaths practice questions for Percentages: reverse (Corbettmaths Video 240), and every card links back to the exact page it came from. Practice tests generate fresh variations of these questions, so the numbers change every attempt. Source material © Corbettmaths — used with attribution.
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If an amount after a 4% increase is £291.20, what calculation finds the original amount?
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Divide by 1.04 (or multiply by 100/104). The original amount is £291.20 ÷ 1.04 = £280.
A population decreased by 2% to 52920. What calculation finds last year's population?
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Divide by 0.98 (or multiply by 100/98). Last year's population was 52920 ÷ 0.98 = 54000.
If 40% of the marbles equals 80 marbles, what is the total number of marbles?
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200 marbles. Calculate 80 ÷ 0.40 = 200.
If 1,020,000 is 2.5% of Canada's population, what is the total population?
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40,800,000. Calculate 1,020,000 ÷ 0.025 = 40,800,000.
A lamp costs £22.05 after a 10% reduction. What was the original price?
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£24.50. After a 10% reduction, the sale price is 90% of the original, so divide by 0.90: £22.05 ÷ 0.90 = £24.50.
A watch costs £84 including 20% VAT. What is the price without VAT?
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£70. The price including VAT is 120% of the original, so divide by 1.20: £84 ÷ 1.20 = £70.
If 96 coffees represent 60% of total hot drinks sold, what is the total number?
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160 hot drinks. Calculate 96 ÷ 0.60 = 160.
Jennifer has 54 books, which is 80% more than last month. How many did she have last month?
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30 books. 54 books represents 180% of last month's amount, so divide by 1.80: 54 ÷ 1.80 = 30.
Lauren's new salary of £24,080 is after a 12% pay rise. What was her original salary?
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£21,500. Her new salary is 112% of the original, so divide by 1.12: £24,080 ÷ 1.12 = £21,500.
A limited edition bag has 25% more flour than standard and contains 650g. How much is in the standard bag?
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520g. The limited edition is 125% of the standard, so divide by 1.25: 650 ÷ 1.25 = 520.
A fish tank has 363 litres remaining after losing 45% of its water. What was the original volume?
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660 litres. 363 litres is 55% of the original, so divide by 0.55: 363 ÷ 0.55 = 660.
A van costs £11,760 including 20% VAT. How much is the VAT amount?
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£1,960. First find the price without VAT: £11,760 ÷ 1.20 = £9,800. Then VAT = £11,760 − £9,800 = £1,960.
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