Percentage change – Intermediate and Higher tier
Increasing or decreasing by a given percentage
- Calculate the percentage given
- Add or subtract the percentage as required
Question
A landlord raises his rental prices by 5%. How much will a two bedroom flat priced at £350 a month cost after the increase?
£367.50
10% of £350 = £35
5% = £17.50
£350 + £17.50 = £367.50
Question
A shop reduces all their stock by 15%. How much would a jacket, costing £60, now cost in the sale?
£51
10% of £60 = £6
5% = £3
15% = £9
£60 - £9 = £51
Finding the original quantity after a percentage increase
Example
A bottle of lemonade advertises that it’s now 50% bigger. If it is now 750 ml, what was its original volume?
Solution
- Start with the original volume as 100%
- The new volume is 50% higher than this; 100% + 50% = 150%
- 150% = 750 ml. We can divide by 150 to find 1%
- 1% = 5 ml. We can now multiply by 100 to find 100%, which was the original volume
- 100% = 500 ml
Question
After a price increase of 9% a television costs £495. How much did it cost originally?
£454.13
109% = £495 (now divide by 109)
1% = 4.541284404
100% = £454.13 (nearest penny)
Finding the original quantity after a percentage decrease
Example
20% of the apples in a harvest are mouldy and are thrown away, leaving 360 good apples. How many were harvested?
Solution
- Start with the original harvest as 100%
- The apples have been reduced by 20%; 100% - 20% = 80%
- 80% = 360 apples. We can divide by 80 to find 1%
- 1% = 4.5 apples. If we now multiply by 100 we will find 100% which is the size of the original harvest
- 100% = 450 apples
Question
60 grams.
100% - 15% = 85%
85% = 51 g (now divide by 85)
1% = 0.6 g (now multiply by 100)
100% = 60g.
