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.

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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?sale

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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 20%.

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Answer

VAT = 20% of £9,999.90

= 20/100 × 9,999.90

= 1,999.98

Since the answer is a price, it must be rounded to two decimal places.

The answer is £1,999.98

Income Tax

People pay tax on the income they earn. The basic rate of income tax is 20% (as of 2011).

VAT

Value Added Tax is added to the cost of most things you buy. It is charged at 20% (as of 2011).

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.

Simple interest

With simple interest the amount of money borrowed remains fixed.

For example £400 is borrowed for 3 years at an interest rate of 5% pa (pa means per annum, or each year).

Interest for one year = 5% of £400

= (5/100 ) × 400

= £20

Interest for 3 years = £20 × 3 = £60.

You can write this in a formula.

Interest = P × R × T

  • P (principal) is the amount borrowed.
  • R is the rate of interest per year.
  • T is the time in years.

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.

Question

Ajay is dealing in electrical goods. He buys a radio for £45 and sells it for £63. What is his percentage profit?

radio

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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?

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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%.

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