Percentage increase and decrease
In some questions you are given the cost price and the selling prices and have to find the percentage increase or decrease. This means you need to find one amount as a percentage of another. You form a fraction from the two amounts and multiply this by 100. Try these questions.
- Question
Ajay is dealing in electrical goods. He buys a radio for £45 and sells it for £63. What is his percentage profit?
- Answer
Here the cost price is £45 and the selling price £63.
The profit is £63 - £45 = £18
To calculate the percentage profit you have to find what the profit is as a percentage of the original price. So divide the profit by the original price and multiply by 100.
18/45 x 100 = 40%.
- Question
Charlotte buys a coat in a sale for £60. The original cost of the coat was £80. What is the percentage decrease?
- Answer
The coat was bought for £60, and the original price was £80.
The decrease is £80 - £60 = £20.
To calculate the percentage decrease, divide the actual decrease by the original price and multiply by 100.
20/80 x 100 = 25%.
Reverse percentages
Sometimes a question will ask you to work backwards and find the original price after an increase.
In Question 1 you were told the original price (the cost price) and the selling price. You were asked to find the percentage profit.
Instead imagine you were given the selling price (£63) and the percentage profit (40%), and told to find the original price.
It would be incorrect to find 40% of £63 and take it away. The 40% is a percentage of the original price, not of the selling price. (40% of £63 happens to be £25.20 which is no help at all.)
The method for questions like this is in Reverse percentages - Higher. If you are given a quantity after a percentage increase or decrease, and you need to find the original amount, use this method.
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