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

Since there is a 20% off sale, then the new price is $0.8\cdot2.50$ . Karl buys five of them, so the amount saved is the price he had to pay with the 20% sale subtracted from the price he had to pay with no sale:

$(5\cdot2.50)-(5\cdot0.8\cdot2.50)=(5\cdot2.50)-(4\cdot2.50)$ $=(5-4)(2.50)$ $=2.50$ $\text{Answer: }\boxed{\mathbf{(C)}}$

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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