# 1952 AHSME Problems/Problem 14

## Problem

A house and store were sold for $\textdollar 12,000$ each. The house was sold at a loss of $20\%$ of the cost, and the store at a gain of $20\%$ of the cost. The entire transaction resulted in: $\textbf{(A) \ }\text{no loss or gain} \qquad \textbf{(B) \ }\text{loss of }\textdollar 1000 \qquad \textbf{(C) \ }\text{gain of }\textdollar 1000 \qquad \textbf{(D) \ }\text{gain of }\textdollar 2000 \qquad \textbf{(E) \ }\text{none of these}$

## Solution

Denote the original price of the house and the store as $h$ and $s$, respectively. It is given that $\frac{4h}{5}=\textdollar 12,000$, and that $\frac{6s}{5}=\textdollar 12,000$. Thus, $h=\textdollar 15,000$, $s=\textdollar10,000$, and $h+s=\textdollar25,000$. This value is $\textdollar1000$ higher than the current price of the property, $2\cdot \textdollar12,000$. Hence, the transaction resulted in a $\boxed{\textbf{(B)}\ \text{loss of }\textdollar1000}$.

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