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Reverse percentages
AQA GCSE Mathematics practice questions with step-by-step solutions
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Sample Questions
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EasyQuestion 1
[2 marks]After a 20% increase, a number becomes 180.
What was the original number?
Solution for Question 1
MediumQuestion 2
[3 marks]In a sale, prices are reduced by 35%.
A coat costs £52 in the sale.
Work out the original price of the coat.
Solution for Question 2
HardQuestion 3
[4 marks]A car's value decreased by 15% in its first year and then by 12% in its second year. After 2 years, the car is worth £14,586.
Work out the original value of the car.
Solution for Question 3
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Reverse percentages find the original value before a percentage change. If you know the final amount after a percentage increase or decrease, you can work backwards to find the original.
The key is to identify what percentage the final amount represents. After a 20% increase, the new amount is 120% of the original. After a 20% decrease, it's 80% of the original.
For example, a sale price of £60 after a 25% discount: £60 represents 75% of the original. So 75% = £60, meaning 1% = £0.80, and 100% = £80. The original price was £80.
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