Percentage change
It is possible to look at the difference between two numbers and work out the percentage increase or the percentage decrease. This is known as percentage change. Often goods are bought for one price and then sold on for another. The percentage change can be calculated to find out the profit or loss an item has made.
Percentage change is calculated by dividing the difference between the two amounts by the original amount.
Example
A brooch is bought at a car boot sale for £40. It is later sold in a shop for £50. What is the percentage profit?
First work out the difference between the two numbers, 40 and 50. The difference between 40 and 50 is 10 (\(50 - 40 = 10\)). Now divide this number by the original number. The brooch was originally bought for £40.
Percentage change = \(\frac{\text{difference}}{\text{original}} = \frac{10}{40} = \frac{1}{4}\) (take out a common factor of 10) = 25%
As the brooch has gone up in price, this is 25% profit.
Question
The number of customers that a food truck receives for lunch drops from 25 to 18 over two days. What is the percentage loss in customers?
First calculate the difference in the two amounts. The difference is 7 customers. (\(25 - 18 = 7\)). The original amount of customers is 25, as this is shown in the question to be the starting number.
Percentage change = \(\frac{\text{difference}}{\text{original}} = \frac{7}{25} = \frac{28}{100}\) (create equivalent fractions to make a denominator of 100)
\(\frac{28}{100} = 28 \%\)
(28 per hundred) so the amount of customers has changed by 28%.
Because the number has dropped from 25 to 18, this is a 28% loss in customer numbers.