Work out reverse percentage problems
The usual question here has to do with sales discounts. For example, a coat is on offer, 25% off. Its sale price is £200. What was the original price before the reduction?
The mistake most people make is find 25% of £200 (£50), add it on, and then say that was the original price: £250.
This is WRONG!
25% was taken off the original price, which was higher than £200. That means the reduction was more than just fifty quid. There are two ways to work out what the original price was. One is the unitary method (also used when calculating with ratios). The other is much simpler if you have a calculator to hand, but less intuitive.
Unitary method – the original price was 100%, and the sale price is 75% of the original.
- 100% Original Price ? 75% Sale Price £200
Divide the sale price by 75 to work out the value of 1% = 200/75 = £2.67.
Multiply 1% by 100 to get 100%, the original price: £2.67 x 100 = £267.
2) The second method is just to convert 75% into a decimal, and then divide the sale price by the decimal number:
£200 / 0.75 = £267
This works because to reduce the original price (P) by 25%, you would multiply it by 0.75
0.75P = 200
So rearranging this equation, we can see that
P = 200/0.75
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