Question

# A merchant placed on display some dresses, each with a marked price. He then posted a sign $\dfrac{1}{3}$ off on these dresses. The cost of the dresses was $\dfrac{3}{4}$of the price at which he actually sold them. Then the ratio of the cost to the marked price was:A.$\dfrac{1}{2}$B.$\dfrac{1}{3}$C.$\dfrac{1}{4}$D.$\dfrac{2}{3}$E.$\dfrac{3}{4}$

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Hint: Use the formula of relation between cost price and selling price.
Selling price = cost price + profit
Selling price = cost price + profit%/100 × cost price
In the profit and loss section, the cost of a product is very crucial. If you have marked the cost of the product wrong, you may not see any profit at all. In the following section, we will see what we mean by marked price. We will also see all the other relevant terms and try to understand how to determine marked price such that the profit is maximum.

Step by step solution:
Marked Price:
The price on the label of an article/product is called the marked price or list price. This is the price at which product is intended to be sold. However, there can be some discount given on this price and the actual selling price of the product may be less than the marked price. It is generally denoted by MP.
When Discount is offered, M.P. > S.P.
When Discount is not offered, M.P. < S.P.
Let the actual cost of dresses = x
Market price of dress = y
Therefore marked price, selling price will be
$=y-\dfrac{y}{3}$
$=\dfrac{3y-y}{3}$
$=\dfrac{2y}{3}$
It is given that cost of the dress was $\dfrac{3}{4}\text{th}$ at which it actually sold then to find Actual cost
We multiply $\dfrac{3}{4}\times \text{selling}\,\,\text{price}$
$x=\dfrac{3}{4}\times \dfrac{2y}{3}$
$x=\dfrac{y}{2}$
$\dfrac{x}{1}=\dfrac{y}{2}$
Using Cross multiplication, we get
$2x=y$
Simplify the equation and rewrite
$\dfrac{x}{y}=\dfrac{1}{2}$

Note:Never get confused with marked price and cost price.Marked price is that price which a shopkeeper would have marked(without any discount) whereas cost price is the actual price at which the shopkeeper would have bought the product.