Percentage Change

Percentages will appear at some point during your GCSE maths exam. You will normally be asked to find a percentage of an amount and then either increase or decrease the amount by that percentage. You could also be asked to work out by what percentage an amount has changed.

Example Question

a) A secondhand car was purchased for £8000. After three years the car's value had decreased by 35%

i) Find 35% of £8000
ii) Find the price of the car after three years.

b) A classic car was bought for £5000. Two years later it was sold in auction for £6500. What is the percentage increase in value?

Solution

a)
i) We begin by finding 10% of £8000 by dividing by 10. So 10% = £800.

Now 5% is half of 10% so 5% = £400
So 35% = 10% + 10% + 10% + 5% = 800 + 800 + 800 + 400 = £2800

Exam tip:
On a calculator paper to find a percentage of an amount you can just multiply by the decimal equivalent of 35% = 0.35.
So 8000 x 0.35 = 2800.

ii) The find the value of the car after three years subtract 35% from the original amount.
£8000 - £2800 = £5200

b)
To find the percentage change we use the formulae:

% change = difference between values x 100%
original value

So the car has gone up in value from £5000 to £6500. This is a difference of £1500.
So the percentage change = 1500 ÷ 5000 x 100 = 30%

Test Yourself!

Find 65% of £340
Increase 80 kg by 20%
An athlete improves his time for running a race from 32 seconds to 28 seconds. What is the percentage change in race time?

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