Question

By selling an article for Rs. 460, a trader gets 15% profit. What is the cost price of the article?
A.Rs. 410
B.Rs. 400
C.Rs. 391
D.Rs. 430

Answer 1

Hint: In this question selling and the gain percentage of the article has already been given so without much calculation, use the formula $ gain\% = \dfrac{{S.P. - C.P.}}{{C.P.}} \times 100 $ to determine the cost price of the article.

Complete step-by-step answer:
In the question, it has already been given that there is a gain in selling the article, so by using the gain percentage formula we will determine the cost price of the article.
Given
Selling price of the article \[S.P. = Rs.460\]
Profit percentage by selling the article \[gain\% = 15\% \]
Now we know the formula $ gain\% = \dfrac{{S.P. - C.P.}}{{C.P.}} \times 100 $
Hence by substituting the values we get
 $
  gain\% = \dfrac{{S.P. - C.P.}}{{C.P.}} \times 100 \\
   \Rightarrow \dfrac{{15}}{{100}} = \dfrac{{S.P. - C.P.}}{{C.P.}} \\
   \Rightarrow \dfrac{{15}}{{100}} = \dfrac{{S.P.}}{{C.P.}} - 1 \\
   \Rightarrow \dfrac{{15}}{{100}} + 1 = \dfrac{{S.P.}}{{C.P.}} \\
   \Rightarrow \dfrac{{S.P}}{{C.P}} = \dfrac{{115}}{{100}} \\
   \Rightarrow C.P = \dfrac{{460 \times 100}}{{115}} \;
  $
By further solving the equation to find the cost price we get $ C.P = \dfrac{{460 \times 100}}{{115}} = Rs.400 $
Hence the cost price of the article $ = Rs.400 $
So, the correct answer is “Option B”.

Note: Many times the marked price of a product is given in the question instead of selling price. So, be careful while reading the question as the marked price is the price which has been marked on the product by the seller but the selling price is the price of the product which the seller actually gets for the product after discount.