A merchant placed on display some dresses, each with a marked price. He then posted a sign “$\frac{1}{3}$ off on these dresses.” 
The cost of the dresses was $\frac{3}{4}$ of the price at which he actually sold them. Then the ratio of the cost to the marked price was: 
$\textbf{(A)}\ \frac{1}{2} \qquad \textbf{(B)}\ \frac{1}{3} \qquad \textbf{(C)}\ \frac{1}{4} \qquad \textbf{(D)}\ \frac{2}{3}\qquad\textbf{(E)}\ \frac{3}{4}$
Let $x$ be the marked price. Then $\frac{2}{3}x$ would be the selling price of the dresses. The cost of the dresses was $\frac{3}{4}$ of the selling price, or $\frac{3}{4}\cdot\frac{2}{3}x \implies \frac{1}{2}x$. So the ratio of the cost to the marked price is $\frac{\frac{1}{2}x}{x}$, or $\frac{1}{2} \implies \boxed{\textbf{(A)}\ \frac{1}{2}}$.