1972 AHSME Problems/Problem 2

Problem

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

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

Solution

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

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1972 AHSME Problems/Problem 2

Problem

Solution