# 1950 AHSME Problems/Problem 23

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## Problem

A man buys a house for $10,000 and rents it. He puts $12\frac{1}{2}\%$ of each month's rent aside for repairs and upkeep; pays$325 a year taxes and realizes $5\frac{1}{2}\%$ on his investment. The monthly rent (in dollars) is:

$\textbf{(A)} \ \ 64.82\qquad\textbf{(B)} \ \ 83.33\qquad\textbf{(C)} \ \ 72.08\qquad\textbf{(D)} \ \ 45.83\qquad\textbf{(E)} \ \ 177.08$

## Solution

$12\frac{1}{2}\%$ is the same as $\frac{1}{8}$, so the man sets one eighth of each month's rent aside, so he only gains $\frac{7}{8}$ of his rent. He also pays $325 each year, and he realizes $5.5\%$, or$550, on his investment. Therefore he must have collected a total of $325 +$550 = \$875 in rent. This was for the whole year, so he collected $\frac{875}{12}$ dollars each month as rent. This is only $\frac{7}{8}$ of the monthly rent, so the monthly rent in dollars is $\frac{875}{12}\cdot \frac{8}{7}=\boxed{\textbf{(B)}\ \ 83.33}$