Question & Answer
QUESTION

A merchant marks his goods up by 75% above his cost price. What is the maximum % discount that he can offer so that he ends up selling at no profit or loss?
A) 75%
B) 47.65%
C) 300%
D) 42.85%

ANSWER Verified Verified
Hint: The marked price is the price at which a product is listed to be sold. The selling price is the price at which a product is actually sold that is the price after the discount is imposed on the marked price of a product. The cost price is the price at which a product is bought.
For no profit and no loss, the selling price and the cost price should be equal.
The formula for finding x percentage of any quantity 1 is
\[\dfrac{x}{100}\times Quantity\ 1\]

Complete step-by-step answer:
As per the question, the merchant has marked the price at 75% above the cost price.
Let the cost price of the product be Rs. 100. As the product is marked at 75% above the cost price, therefore, the marked price of the product is
\[\begin{align}
  & =\dfrac{75}{100}\times 100+100 \\
 & =Rs.175 \\
\end{align}\]
Hence, the marked price is Rs. 175.
Now, for no profit and no loss, the product should be sold at the same price as the cost price should be equal to the selling price.
So, as selling price=Rs. 100, the discount should be of Rs. 75.
Hence, the discount percentage is
=\[{\dfrac{75}{175}\times 100}%\]
=\[{\dfrac{300}{7}}%\]
=\[{42.85}%\]
(Because the discount percentage is always taken over the marked price)
Hence, the discount percentage is 42.85%.

Note: Another way of doing this particular type of question is that we can assume the cost price to be x and then proceed the same procedure as given in the above solution.
The only step at which the student can make an error is where the discount percentage is to be calculated as marked price is to be taken into account rather than selling price. Hence, taking the cost price as Rs.100 is advisable.