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Unit A2 Section 7
Percentage Increase and Decrease

Percentage increases are calculated using

Percentage increase = × 100%

Similarly, percentage decreases are calculated using

Percentage decrease = × 100%

Worked Examples

1

The population of a village increased from 234 to 275 during one year. Find the percentage increase.

Actual increase = 275 − 234 = 41
Percentage increase = × 100%
= 17.52%   (to 2 decimal places)
2

When a beaker of sand is dried in a hot oven its mass reduces from 450 grams to 320 grams. Find the percentage reduction in its mass.

Actual reduction = 450 grams − 320 grams
= 130 grams
Percentage reduction = × 100%
= 28.9%
3

John buys pens for £5 each and then sells them to other students for £6.90. Find his percentage profit.

Actual profit = £6.90 − £5
= £1.90
Percentage profit = × 100%
= 38%

Exercises

Give answers to 1 decimal place where necessary.

A baby weighed 5.6 kg and six weeks later her weight had increased to 6.8 kg.
Find the percentage increase.

%

A factory produces pens at a cost of 88 euro cents and sells them for 1.10 euros Find the percentage profit.

%

A boat which cost £1500 was sold one year later for £999.50. Find the percentage reduction in the value of the boat.

%

An investor bought some shares at a price of £4.88 each. The price of the shares dropped to £3.96 each. Find the percentage loss.

%

A supermarket offers a £10 discount to all customers spending £40 or more. Kate spends £42.63 and John spends £78.82. Find the percentage saving for each of these customers.

Kate has a % saving and John has a % saving.
(a)

Derek bought a hose marked at £35. How much did he save?

He saved £
(b)

Kenton needs a large plant pot. He can buy pot A which is marked £27.95 or pot B which is marked £32.45.

(i)

Calculate 20% of £32.45.

£
(ii)

How much cheaper would it be for Kenton to buy pot B than to buy pot A?

It would be £ cheaper.
(c)

Kenton's wife suggests that he buys pot A, together with some seeds costing £2.05 which he doesn’t want, so that he gets the 20% saving.

If he buys the seeds and pot A, express his saving as a percentage of the cost of pot A.

%
(a)

Work out the sale price of the Super Ace Games System.

Sale price: £
(b)

Find the percentage reduction on the Mega Ace Games System in the sale.

% reduction

Leon paid £7.20 for a wallet. He sold it for £6.30. What was his loss as a percentage of the price he paid?

%