1955 AHSME Problems/Problem 7

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Problem

If a worker receives a $20$% cut in wages, he may regain his original pay exactly by obtaining a raise of:

$\textbf{(A)}\ \text{20\%}\qquad\textbf{(B)}\ \text{25\%}\qquad\textbf{(C)}\ 22\frac{1}{2}\text{\%}\qquad\textbf{(D)}\ \textdollar{20}\qquad\textbf{(E)}\ \textdollar{25}$

Solution

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 $\boxed{\mathrm{bf{(B)} 137^\circ 30'}}$.