Home > Maths II > Numbers and money > Reverse percentages

Maths II

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 -

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

**Solution**

Start with the original amount as 100%.

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 = .

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.

Now try a Test Bite

BBC © 2014 The BBC is not responsible for the content of external sites. Read more.

**This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.**