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Home > Maths II > Numbers and money > Reverse percentages

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.

A photo of a modern style radio.

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 100 \% + 40 \% = 140 \% of the cost price.

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

Now calculate 1%:

140 \% = \pounds 63

1 \% = \pounds 63/140

1 \% = \pounds 0.45

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

Cost price = 0.45 \times 100 = \pounds 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 \pounds 8,400 = 70 \% of the original price.

So 1% of original price = \pounds 8,400 \div 70

Original price = 100 \% = 100 \times 1 \% = 100 \times (\pounds 8,400 \div 70)

= \pounds 12,000.

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

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