1951 AHSME Problems/Problem 5

Problem 5

Mr. $A$ owns a home worth $$$$ 10,000. He sells it to Mr. $B$ at a 10% profit based on the worth of the house. Mr. $B$ sells the house back to Mr. $A$ at a 10% loss. Then:

$\mathrm{(A) \ A\ comes\ out\ even } \qquad$ $\mathrm{(B) \ A\ makes\ 1100\ on\ the\ deal}$ $\qquad \mathrm{(C) \ A\ makes\ 1000\ on\ the\ deal } \qquad$ $\mathrm{(D) \ A\ loses\ 900\ on\ the\ deal }$ $\qquad \mathrm{(E) \ A\ loses\ 1000\ on\ the\ deal }$

Solution

Mr. $A$ earns $1.1\cdot$ <dollar/> $10,000=$ <dollar/> $11,000$ after he sells it to Mr. $B$ . Then, Mr. $B$ sells it at a price of $(1-0.1)\cdot$ <dollar/> $11,000=$ <dollar/> $9,900$ , so Mr. $A$ ultimately earns $\boxed{\textbf{(B)}}$ <dollar/> $1,100$ .

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1951 AHSME Problems/Problem 5

Problem 5

Solution