Question

What is the percent change of $120$ to $90$?

Answer 1

Hint: The change in percentage can be in two ways, either increasing or decreasing. To know about what kind of percentage change is this, along with the percent of change, use the formula $\% change = \dfrac{{change(amount)}}{{original(amount)}} \times 100\% $, where change represents the difference between original and new value. Just put the values and get the answer.

Formula Used:
$\% change = \dfrac{{change(amount)}}{{original(amount)}} \times 100\% $
$\dfrac{{change(amount)}}{{original(amount)}} = \dfrac{{New - Original}}{{Original}}$
“Percent” is represented as “$\% $” which means “out of $100$” or “per $100$”.
Cent means $100$.

Complete step by step solution:
We are given a number $120$, which has now changed to $90$, that means there is a decrease in the value which would lead to decrease in the percentage also.
So, the original amount was: $120$.
And the change in value becomes: New Value-Original Value, and we get:
$
   = 90 - 120 \\
   = - 30 \\
 $
Since, we are looking for the change which is always positive in value, so, we would write the absolute value of the change and we get:
$change = \left| { - 30} \right| = 30$
For the change in percentage we know the formula, which is $\% change = \dfrac{{change(amount)}}{{original(amount)}} \times 100\% $.
Substituting the change(amount) $ = 30$ and original(amount) $ = 120$ in the above equation and we get:
$
  \% change = \dfrac{{change(amount)}}{{original(amount)}} \times 100\% \\
   = \dfrac{{New - Original}}{{Original}} \times 100\% \\
   = \dfrac{{30}}{{120}} \times 100\% \\
 $
On further solving, we get:
$
   = \dfrac{{30}}{{120}} \times 100\% \\
   = \dfrac{1}{4} \times 100\% \\
   = 25\% \\
 $
Since, we knew that the percentage was decreasing, that means there is $25\% $ decrease in the value.

Therefore, the percent change of $120$ to $90$ is $25\% $ decrease.

Note:
1) If the new number is greater than the original number (increasing the quantity), then change will be positive and the change in percentage would be increased.
2) Do not write the value of change in negative, it’s only to know whether the value is increasing or decreasing. Always change the negative value into their absolute value.