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:
$\textbf{(A) \ }20  \qquad \textbf{(B) \ }100 \qquad \textbf{(C) \ }125 \qquad \textbf{(D) \ }80 \qquad \textbf{(E) \ }120$
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 $\boxed{\textbf{(C)}\ 125}$.