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

Start with the original amount as 100%.

Cost price = 100%

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

So the selling price is 100% + 40% = 140% of the cost price.

We know that the selling price is £63, so 140% = £63.

Now calculate 1%:

140% = £63

1% = £63/140

1% = £0.45

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

Cost price = 0.45 × 100 = £45.

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 = 100% - 30% = 70%.

So £8,400 = 70% of the original price.

So 1% of original price = £8,400 ÷ 70

Original price = 100% = 100 x 1% = 100 x (£8,400 ÷ 70)

= £12,000.

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