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Maths II

Reverse percentages

# Reverse percentages

Sometimes a question will ask you to work backwards and find the original price of something after the price has increased. If you are given a quantity after a percentage increase or decrease, and you need to find the original amount, use this method -

## Example 1

A radio sells for £63, after a 40% increase in the cost price. Find the cost price.

Solution

Cost price = 100%

We are told the selling price is a 40% increase in the cost price.

So the selling price is of the cost price.

We know that the selling price is £63, so

Now calculate 1%:

The cost price is 100%, so multiply £0.45 by 100.

Cost price = .

## Example 2

A new car falls in value by 30% in a year. After a year, it is worth £8,400.

Find the price of the car when it was new.

Solution

Remember that the original price of the car is 100%.

Original price = 100%.

Second-hand price =

So of the original price.

So 1% of original price =

Original price =

= .

It is easy to go wrong in this type of question. Always check that your answer is realistic.

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