Percent change (increase or decrease) from an original value to a new value frequently occurs.
To find the percent change, first find the amount of the change, then divide this amount by the original value, and finally express this quotient as a percent.
For example if the price of an item changes from $32 to $40, the amount of the increase is $(40 − 32) = $8 and the percent increase is 8/32 = 1/4 = 0.25 = 25%.
On the other hand, if the price of the item changes from $40 to $32, the amount of the decrease is $(40 − 32) = $8 and the percent decrease is 8/40 = 1/5 = 0.2 = 20%.
Interestingly, the percent increase from 32 to 40 is different from the percent decrease from 40 to 32.
Example
A vehicle manufacturer sold 7000 cars in 2002. If the car sales decreased by 13.5% in 2003, how many cars did the manufacturer sell in 2003? Solution.
13.5% of 7000 = 0.135 × 7000 = 945
So, cars sold in 2003 were 7000 − 945 = 6055
Alternatively, a decrease of 13.5% implies the cars sold in 2003 were 86.5% of the cars sold in 2002.
So, cars sold in 2003 were 86.5% of 7000 = 0.865 × 7000 = 6055
Percent changes can be greater than 100%.
Example
a) If the price of a certain share on the stock market is 400% of its price a year ago, what is the percent increase in the price?
b) If the price of some other share on the stock market a year ago was 400% of the current price, what is the percent decrease in the price? Solution.
a)
Let P be the share price a year ago, then the current price is 4P.
So, the amount of the increase is $(4P − P) = $3P.
Therefore, the percent increase is 3P/P = 3 = 300%.
b)
Let P be the current share price, then 4P was the price a year ago.
So, the amount of the decrease is $(4P − P) = $3P.
Therefore, the percent decrease is (3P)/(4P) = 3/4 = 0.75 = 75%.
Note that P may be chosen to be 100 to simplify calculations.
In general, when a price changes n times, the percent change is (n − 1) × 100%.
For example, when n = 4, percent change (increase) = (4 − 1) × 100% = 300%
For example, when n = 1/4, percent change (decrease) = (1/4 − 1) × 100% = 75%
