1952 AHSME Problems/Problem 14

Revision as of 19:09, 19 December 2017 by Wintermath (talk | contribs) (Solution)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

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 $\boxed{\textbf{(B)}\ \text{loss of }\textdollar1000}$.

See also

1952 AHSC (ProblemsAnswer KeyResources)
Preceded by
Problem 13
Followed by
Problem 15
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50
All AHSME Problems and Solutions

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. AMC logo.png