Maths
Percentages
'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.
Finding percentages
A percentage is a fraction of 100.
30% (30 in each 100) as a fraction is 30/100
30% as a decimal is 0.3.
Often, in real life - and maths exams - you must find a percentage of a quantity. First, write the percentage as a fraction or a decimal, then multiply by the quantity.
Have a look at this question:
- Question
Find 40% of £50.
- Answer
First, write 40% as a fraction: 40% = 40/100 = 4/10 = 2/5
Now multiply by the quantity:
2/5 × 50 = £20.
Practise converting percentages to fractions. Then try the questions below.
- Question
Sarah is buying a pair of jeans. The original price was £75, but there is a discount of 30%. How much will the discount be?
- Answer
Discount = 30% of 75
= 30/100 × 75
= 0.3 × 75
= £22.50
(Note that if the question asked for the discount price, you would subtract the discount from the original price : £75 - £22.50 = £52.50.)
Sometimes both the percentage and amount of money will not be whole numbers.
- Question
A car costs £9,999.90 before VAT (value added tax). Work out the cost of the VAT if it is charged at 17.5%.
- Answer
VAT = 17.5% of £9,999.90
= 17.5/100 × 9,999.90
= 1,749.9825
Since the answer is a price, it must be rounded to two decimal places.
The answer is £1,749.98
Profit and loss
People often buy something at one price, and sell it on for another - eg, when they are selling things at a car boot sale.
If the selling price is greater than the buying price, a profit is made.
If the selling price is less than the buying price, there is a loss
Income Tax
People pay tax on the income they earn. The basic rate of income tax is 22%.
VAT
Value Added Tax is added to the cost of most things you buy. It is charged at 17.5%.
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.
Now try a Test Bite