Difference between revisions of "1955 AHSME Problems/Problem 7"

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==Solution==
 
==Solution==
Since the worker receives a <math>20</math>% cut in wages, his present wage would be <math>\frac{4}{5}</math> of the original wage before the cut. To regain his original pay he would have to obtain a raise of <math>1</math>\div<math>\frac{4}{5}</math> = <math>\ 1\\frac{1}{4}</math>.
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Since the worker receives a <math>20</math>% cut in wages, his present wage would be <math>\frac{4}{5}</math> of the original wage before the cut. To regain his original pay he would have to obtain a raise of <math>1</math> <math>\div</math> <math>\frac{4}{5}</math> = <math>1</math><math>\frac{1}{4}</math>.
Therefore, the worker would have to get a <math>\boxed{\mathrm{bf{(B)} 137^\circ 30'}}</math>.
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Therefore, the worker would have to get a <math>\fbox{{\bf(B)} 25\%}</math> raise.

Revision as of 05:37, 8 July 2018

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 $\fbox{{\bf(B)} 25\%}$ raise.