Multiple choice

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 :

  1. $\frac{1}{2}$
  2. $\frac{1}{3}$
  3. $\frac{1}{4}$
  4. $\frac{2}{3}$
  5. $\frac{3}{4}$
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A Correct answer
Explanation

Let M be the marked price. Selling price S = (2/3)M. Cost C = (3/4)S = (3/4) * (2/3)M = (1/2)M. The ratio C/M = 1/2.

AI explanation

Let the marked price be 300. A discount of 1/3 off means the selling price is 300 - 100 = 200. The cost is 3/4 of this selling price, which is 3/4 of 200, giving a cost of 150. The ratio of the cost to the marked price is 150 : 300, which simplifies to 1/2.

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