1964 AHSME Problem 9

A jobber buys an article at \$24 less 12\frac{1}{2}\%. He then wishes to sell the article at a gain of 33\frac{1}{3}\% of his cost after allowing a 20\% discount on his marked price. At what price, in dollars, should the article be marked?

\textbf{(A)}\ 25.20 \qquad \textbf{(B)}\ 30.00 \qquad \textbf{(C)}\ 33.60 \qquad \textbf{(D)}\ 40.00 \qquad \textbf{(E)}\ \text{none of these}

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.