GCSE Maths revision · Ratio and proportion

Reverse percentages

Foundation and Higher

The idea

After a percentage change you can find the original by dividing by the multiplier. If a price after a $20\%$ rise is $\text{£}72$ , the original is $72 \div 1.2 = \text{£}60$ .

Write the multiplier for the change: up $20\%$ is $1.2$ , down $20\%$ is $0.8$ .
Divide the new amount by the multiplier.
Simple interest is the same amount each year: $\text{£}500$ at $3\%$ for $4$ years earns $4 \times \text{£}15 = \text{£}60$ .

Watch out Do not take $20\%$ of the new price off: $20\%$ of $\text{£}72$ is not the rise.

See it worked

Worked exampleNon-calculator3 marks

£600 is invested at 3% simple interest per year for 4 years. Work out the total interest earned.

$600\times 0.03$
$18\times 4$
Simple interest uses the original £600 each year.
600 $\times$ 0.03 $\times$ 4 = £72 interest.

Answer £ $72$

Your turn

Question 1Calculator allowed4 marks

You may use a calculator.

(a) Nadia invests £2400 for 5 years at $3\%$ per year simple interest. Work out the total interest she earns.

(b) A trader buys a lamp for £40 and sells it for £52. Work out the percentage profit.

Question 2Calculator allowed4 marks

You may use a calculator.

(a) In a sale, the price of a television is reduced by $15\%$ . The sale price is £323. Work out the price before the sale.

(b) Ravi's rent went up by $4\%$ . His new rent is £832 per month. What was his rent before the increase?

Question 3Non-calculator1 mark

A price is increased by p%, where p > 0. It is then reduced by q% to return exactly to its original value. Which expression gives q in terms of p? Select one answer.

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