1950 AHSME Problems/Problem 36

Problem

A merchant buys goods at $25\%$ off the list price. He desires to mark the goods so that he can give a discount of $20\%$ on the marked price and still clear a profit of $25\%$ on the selling price. What percent of the list price must he mark the goods?

$\textbf{(A)}\ 125\% \qquad \textbf{(B)}\ 100\% \qquad \textbf{(C)}\ 120\% \qquad \textbf{(D)}\ 80\% \qquad \textbf{(E)}\ 75\%$

Solution

Without loss of generality, we can set the list price equal to $100$ . The merchant buys the goods for $100*.75=75$ . Let $x$ be the marked price. We then use the equation $0.8x-75=25$ to solve for $x$ and get a marked price of $\boxed{125}$ .

$\text{Answer: }\boxed{\mathbf{(A)}}$

1950 AHSC (Problems • Answer Key • Resources)
Preceded by Problem 35	Followed by Problem 37
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1950 AHSME Problems/Problem 36

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