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Reverse Percentages

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Lesson

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Flow diagram showing a 5% increase from £200 to £210 using ×1.05 and reverse ÷1.05, and a 20% decrease from £35 to £28 using ×0.80 and reverse ÷0.80

Reverse percentages ask you to find the amount before a percentage change. First identify the original amount, the final amount, and whether the change was an increase or a decrease.

The forward rule is:

F=O×m F = O \times m F=O×m

where mmm is the multiplier. To work backwards, use the inverse formula:

O=Fm O = \frac{F}{m} O=mF​

For an increase, the multiplier is more than 111, like 1.101.101.10 for a 10%10\%10% increase. For a decrease, the multiplier is less than 111, like 0.800.800.80 for a 20%20\%20% decrease.

Questions

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36 exam-style questions

Practice questions

Question 1

2 marks

The value of a house increased by 6%.
The house then had a value of £265 000

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In reverse percentages, the percentage change is based on which amount?

Reverse Percentages Revision Guide

  1. GCSE
  2. /Maths
  3. /Reverse Percentages

Revision notes for Edexcel GCSE Maths Reverse Percentages. Open the guide for explanations and worked examples. Written against the Edexcel GCSE Maths (1MA1) specification, so the content matches what's examinable rather than general Maths background.

Revision guides

Practise questions

1 of 5

After a 25% reduction, a pair of trainers costs £36. What was the original price?