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 $\frac{5s}{4}=\textdollar 12,000$ . 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 $\boxed{\textbf{(B)}\ \text{loss of }\textdollar1000}$ .

1952 AHSC (Problems • Answer Key • Resources)
Preceded by Problem 13	Followed by Problem 15
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1952 AHSME Problems/Problem 14

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