6 - Reverse percentages
You may be asked to find the original price of an item after the price has increased or decreased. If you are given a quantity after a percentage increase or decrease, you can calculate the original price of the item by following this method:
(a) A stereo sells for £120 after a 25% increase in the cost price. Calculate the original cost price of the stereo.
(a) Regard the original cost price of the stereo as 100%.
The selling price is a 25% increase of this cost price. Therefore the selling price is :
100% + 25% = 125% of the cost price
The question tells you that the selling price is £120, so 125% = £120
To calculate the original price, first calculate 1% of the cost of the stereo:
125% = £120, so 1% will be 120/125= 0.96
1% = £0.96
The original cost price is 100%, so multiply £0.96 by 100
Therefore the original cost price of the stereo = 0.96 × 100 = £96.
(b) The cost of a new DVD decreases in price by 20% in a year. After a year the DVD is worth £10. Calculate the original cost price of the DVD when it was new.
(b) The original cost price of the DVD is 100%.
The decreased price = 100%- 20% = 80%
So £10 = 80% of the original cost price of the DVD
From this value you can work out that 1% of original price = £10 ÷ 80
Therefore the original cost price of the DVD = 100% = 100 x 1% = 100 x (£10 ÷ 80)
Therefore the original cost price of the DVD = £12.50.