Percentages 2
Fractions and Percentages of Quantities

Percentages are often used to describe changes in quantities or prices. For example,

'30% extra free''10% discount''add 16% VAT'

This section deals with finding fractions or percentages of quantities.

Worked Examples

1

Find 20% of £84.

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This can be done by converting 20% to either a fraction or a decimal.

Converting to a fraction

Note that20% = =
Therefore
20% of £84 = × £84
= £16.80

Converting to a decimal

Note that20% = 0.2
Therefore
20% of £84 = 0.2 × £84
= £16.80
2

A shopkeeper decides to increase some prices by 10%. By how much would she increase the price of:

First note that 10% = .

(a)

a bar of soap costing 90 pence

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10% of 90 p = × 90 p
= 9 p

So the cost of a bar of soap will be increased by 9 pence
(b)

a packet of rice costing £2.00?

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10% of £2 = × £2
= £0.20 or 20 p

So the cost of a packet of rice is increased by 20 pence.
3

A farmer decides to sell 25% of his herd of 500 cattle. How many cows does he sell?

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First note that 25% = .

25% of 500 = × 500
= 125

So he sells 125 cows.
4

Natasha invests £20 000 in a building society account. At the end of the year she receives 5% interest. How much interest does she receive?

Show me

First convert 5% to a fraction.

5% = =

5% of £20 000 = × £20 000
= £1000

So she receives £1000 interest.

Exercises

Find

(a)
10% of 200
(b)
50% of £5 £
(c)
20% of £8 £
(d)
25% of £10 000 £
(e)
40% of £500 £
(f)
90% of 200
(g)
33 % of £12 £
(h)
75% of 800
(i)
75% of 1000
(j)
80% of 20 kg kg
(k)
70% of 5 kg kg
(l)
30% of 50 kg kg
(m)
5% of 100 m m
(n)
20% of 50 m m
(o)
25% of £30 £

Find

(a)
of 80
(b)
of 120
(c)
of 90
(d)
of 360
(e)
of 150
(f)
of 500

A firm decides to give 20% extra free in their packets of soap powder. How much extra soap powder would be given away free with packets which normally contain

(a)

2 kg of powder

g
(b)

1.2 kg of powder?

g

A picture costs £30 000. A buyer is given a 10% discount. How much money does the buyer save?

£

John has invested £500 in a building society. He gets 5% interest each year. How much interest does he get in a year?

£

Kina's mother decided to increase her pocket money by 40%. How much extra did Kina receive each week if previously she had been given £4.00 per week?

£

A newborn baby girl weighed 4 kg. In the first three months her weight increased by 60%. How much weight had the baby gained?

kg

An athletics stadium has 35 000 seats. 4% of the seats are fitted with headphones to help people hear the announcements. How many headphones are there in the stadium?

headphones