# 1955 AHSME Problems/Problem 26

Mr. $A$ owns a house worth $\textdollar{10000}$. He sells it to Mr. $B$ at $10$% profit. Mr. $B$ sells the house back to Mr. $A$ at a $10$% loss. Then: $\textbf{(A)}\ \text{Mr. A comes out even}\qquad\textbf{(B)}\ \text{Mr. A makes } \textdollar{ 100}\qquad\textbf{(C)}\ \text{Mr. A makes } \textdollar{ 1000}\\ \textbf{(D)}\ \text{Mr. B loses } \textdollar{ 100}\qquad\textbf{(E)}\ \text{none of the above is correct}$

## Solution

Assume that Mr. $A$ has $\textdollar{10000}$ to start with (the house) and Mr. $B$ has $\textdollar{11000}$ $A$ sells the house to $B$ for $\textdollar{11000}$, leaving Mr. $A$ with $\textdollar{11000}$ and Mr. $B$ with $\textdollar{10000}$.

Then, Mr. $B$ sells the house back to Mr. $A$ for $\textdollar{9000}$, which leaves $A$ with $\textdollar{12000}$ and $B$ with $\textdollar{9000}$.

We can see that $A$ gained $\textdollar{2000}$ out of Mr. $B$'s expense, but none of the options says this. We can therefore conclude that the correct answer is $\boxed{\textbf{(C)}}$.

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