# 1952 AHSME Problems/Problem 17

## Problem

A merchant bought some goods at a discount of $20\%$ of the list price. He wants to mark them at such a price that he can give a discount of $20\%$ of the marked price and still make a profit of $20\%$ of the selling price. The per cent of the list price at which he should mark them is: $\textbf{(A) \ }20 \qquad \textbf{(B) \ }100 \qquad \textbf{(C) \ }125 \qquad \textbf{(D) \ }80 \qquad \textbf{(E) \ }120$

## Solution

Let $C$ represent the cost of the goods, and let $L$, $S$, and $M$ represent the list, selling, and marked prices of the goods, respectively. Hence, we have three equations, which we need to manipulate in order to relate $M$ and $L$: $C=\frac{4}{5}L$ $S=C+\frac{1}{5}S$ $S=\frac{4}{5}M$

We find that $M=\frac{5}{4}L$. Hence, the percent of the list price which should be marked is $\boxed{\textbf{(C)}\ 125}$.

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