Percentage change - WJECPercentage increase and decrease
Percentages can be used to increase or decrease a quantity relative to its size. Shops reduce their goods by a percentage and the government increases the cost of goods by adding on a percentage tax.
Percentage increase and decrease - Intermediate and Higher tier
You may also need to increase a value by a given percentage. In this case, add on the percentage change. Read the question carefully so that you know whether you are increasing or decreasing the amount.
Question
zs7gk7h Cai's rent is increasing by 3.1% from £460 per calendar month (pcm). Elin's landlord is giving her a reduction of 3.5% on her calendar monthly rent of £484. What will they each be paying in rent after these changes?
Cai
£460 ÷ 100 × 3.1 = £14.26 increase
New rent – £460 + £14.26 = £474.26 pcm
Elin
£484 ÷ 100 × 3.5 = £16.94 decrease
New rent – £484 − £16.94 = £467.06 pcm
There is an alternative way of calculating the new rents.
Cai
Increase is 3.1%, so new rent is 103.1% of the original rent.
103.1% of £460 = £460 ÷ 100 × 103.1 = £474.26
Cai's new rent is £474.26 pcm.
Elin
Decrease is 3.5%, so new rent is 96.5% of original rent.
96.5% of £484 = £484 ÷ 100 × 96.5 = £467.06.
Elin's new rent is £467.06 pcm.
Calculating the original value after a discount has been applied may be useful to find out what the item was priced at before.
Example
A shirt has been reduced by 20% and now costs £50. How much did it cost originally?
Solution
Taking the original price to be 100% we can see that the sale price is 80% of this value because 100% − 20% = 80%.
100% − 20% = 80%.
£50 = 80%.
Divide both sides by 80 to find 1%.
£0.625 = 1%.
Multiply both sides by 100 to find the original price.
Original price is £62.50.
We can check this by working out 80% of the original price, and checking that it is the sale price.
80% of £62.50 = £62.50 ÷ 100 × 80 = £50, which is correct.
