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# What is a reverse percentage?

By Lisa Kelly on the 11th of June, 2012

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# 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% 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.

By Pinaki Panda on the 16th of January, 2013

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Oh well I wish I could let you know but I do not know myself. You should probably check out various british assignment writers in the regard. You will be surprised to realize how helpful it could all be.

By Garvyn on the 21st of February, 2018

## This is WRONG!

### Unitary method – the original price was 100%, and the sale price is 75% of the original.

1. 100% Original Price ? 75% Sale Price £200

### P = 200/0.75

Nothing in this section yet. Why not help us get started?

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