The length of a rectangle is increased by $25\%$, but the width of the rectangle is decreased to keep the area of the rectangle  unchanged.  By what percent was the rectangle's width  decreased?
I know that the area of a rectangle is given by the formula $A = lw$, where $l$ is the length and $w$ is the width. Since the area is unchanged, I can write an equation that relates the original length and width to the new length and width. Let $l$ and $w$ be the original length and width, and let $l'$ and $w'$ be the new length and width. Then, the equation is $lw = l'w'$. I also know that the length was increased by $25\%$, which means that $l' = 1.25l$. I can substitute this into the equation and simplify: $lw = 1.25lw' \implies w = 1.25w' \implies w' = \frac{w}{1.25}$. This means that the new width is $\frac{1}{1.25} = 0.8$ times the old width. Therefore, the width was decreased by $1 - 0.8 = 0.2 = 20\%$. 