Percentages - Higher
'Percent' means 'out of 100'. If 90 per cent of the population owns a mobile phone, this means 90 out of every 100 people have one. The symbol '%' means per cent.
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:
A radio sells for £63, after a 40% increase in the cost price. Find the cost price.
Start with the original amount as 100%.
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.
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.
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)
It is easy to go wrong in this type of question. Always check that your answer is realistic.
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