# Is the percent increase from 25 to 100 the same as the percent decrease from 100 to 25?

Dec 22, 2016

No

#### Explanation:

$\text{increase in value" = "new value" - "original value}$
The percentage increase is
color(white)("XXX")("increase in value")/("orignal value")xx100%

In this case, the percentage increase is
color(white)("XXX")(100-25)/(25)xx100%=300%

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$\text{decrease in value" = "original value" - "new value}$
The percentage decrease is
color(white)("XXX")("decrease in value")/("original value")xx100%

In this case, the percentage decrease is
color(white)("XXX")(100-25)/100xx100%=75%