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?
Answer
- 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% = 100 x 4.5 = 450 apples
- The total number of apples harvested was 450.
Question
Start with the original weight as 100%.
The new weight is an increase of 15%.
100% - 15% = 85%
85% = 51 g
1% = 0.6 g
100% = 60g
The original packet weight was 60 g.
Calculating the original value after a discount has been applied may be useful to find out what the item was priced at before.
Question
A shirt has been reduced by 20% and now costs £50. How much did it cost originally?
Taking the original price to be 100% we can see that the sale price is 80% of this value because 100% − 20% = 80%.
£50 = 80%.
1% = £50 ÷ 80 = £0.625.
100% = 100 x £0.625 = £62.50
The original price was £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.
