If a worker receives a $20$% cut in wages, he may regain his original pay exactly by obtaining a raise of:
$\textbf{(A)}\ \text{20\%}\qquad\textbf{(B)}\ \text{25\%}\qquad\textbf{(C)}\ 22\frac{1}{2}\text{\%}\qquad\textbf{(D)}\ \textdollar{20}\qquad\textbf{(E)}\ \textdollar{25}$
Since the worker receives a $20$% cut in wages, his present wage would be $\frac{4}{5}$ of the original wage before the cut. To regain his original pay he would have to obtain a raise of $1$ $\div$ $\frac{4}{5}$ = $1$$\frac{1}{4}$.
Therefore, the worker would have to get a $\fbox{{\bf(B)} 25\%}$ raise to acquire his original pay.
Solution by awesomechoco