1972 AHSME Problems/Problem 2


If a dealer could get his goods for $8$% less while keeping his selling price fixed, his profit, based on cost, would be increased to $(x+10)$% from his present profit of $x$%, which is

$\textbf{(A) }12\%\qquad \textbf{(B) }15\%\qquad \textbf{(C) }30\%\qquad \textbf{(D) }50\%\qquad  \textbf{(E) }75\%$


If $c$ is the cost, then $0.92c$ is the reduced cost. Selling price is equal to cost plus profit:

\[c(1+0.01x) = 0.92c(1 + 0.01(x+10))\]

Solving for $x$ yields $x = 15.$ The answer is $\textbf{(B)}.$

-edited by coolmath34