1951 AHSME Problems/Problem 5

Revision as of 15:06, 1 February 2009 by Math154 (talk | contribs) (Solution)

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 $\boxed{\textbf{(B)}\ \text{A makes 1100 on the deal}$ (Error compiling LaTeX. Unknown error_msg).