A merchant placed on display some dresses, each with a marked price. He then posted a sign “ 13 off on these dresses.” The cost of the dresses was 34 of the price at which he actually sold them. Then the ratio of the cost to the marked price was:

1954 AMC 12 Problem 11

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11.

A merchant placed on display some dresses, each with a marked price. He then posted a sign “

\dfrac13

off on these dresses.” The cost of the dresses was

\dfrac34

of the price at which he actually sold them. Then the ratio of the cost to the marked price was:

\dfrac12

\dfrac13

\dfrac14

\dfrac23

\dfrac34

The selling price is

\frac{2}{3}

of the marked price

The cost is

\frac{3}{4}

of that selling price

If the marked price is

M,

then the selling price is

\frac{2M}{3}.

The cost is therefore

\frac34\cdot\frac23M=\frac12M.

The cost-to-marked-price ratio is

\frac{1}{2}.

Thus, the correct answer is A.