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Difference between revisions of "1952 AHSME Problems/Problem 14"

(Created page with "== Problem== A house and store were sold for <math> \textdollar 12,000 </math> each. The house was sold at a loss of <math> 20\% </math> of the cost, and the store at a gain of <...")
 
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==Solution==
 
==Solution==
  
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Denote the original price of the house and the store as <math> h </math> and <math> s </math>, respectively. It is given that <math> \frac{4h}{5}=\textdollar 12,000 </math>, and that <math> \frac{5s}{4}=\textdollar 12,000 </math>. Thus, <math> h=\textdollar 15,000 </math>, <math> s=\textdollar10,000 </math>, and <math> h+s=\textdollar25,000 </math>. This value is <math> \textdollar1000 </math> higher than the current price of the property, <math> 2\cdot \textdollar12,000 </math>. Hence, the transaction resulted in a <math> \boxed{\textbf{(B)}\ \text{loss of }\textdollar1000} </math>.
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Denote the original price of the house and the store as <math> h </math> and <math> s </math>, respectively. It is given that <math> \frac{4h}{5}=\textdollar 12,000 </math>, and that <math> \frac{6s}{5}=\textdollar 12,000 </math>. Thus, <math> h=\textdollar 15,000 </math>, <math> s=\textdollar10,000 </math>, and <math> h+s=\textdollar25,000 </math>. This value is <math> \textdollar1000 </math> higher than the current price of the property, <math> 2\cdot \textdollar12,000 </math>. Hence, the transaction resulted in a <math> \boxed{\textbf{(B)}\ \text{loss of }\textdollar1000} </math>.
  
 
==See also==
 
==See also==
 
{{AHSME 50p box|year=1952|num-b=13|num-a=15}}
 
{{AHSME 50p box|year=1952|num-b=13|num-a=15}}
 
{{MAA Notice}}
 
{{MAA Notice}}

Latest revision as of 20:09, 19 December 2017

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 (Problems • Answer Key • Resources)
Preceded by
Problem 13 		Followed by
Problem 15
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All AHSME Problems and Solutions

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