Question

Praveen sold an article for Rs. 475 at some profit. Had he sold it for Rs. 325, he would have incurred the same amount of loss. What is the cost price of the article?
(a) Rs. 400
(b) Rs. 350
(c) Rs. 375
(d) Cannot be determined
(e) None of these

Answer 1

Hint: We solve this problem by using the formulas of profit and loss.
If C.P is the cost price and the S.P is the selling price of an article then
\[\text{Profit}=S.P-C.P\]
If C.P is the cost price and the S.P is the selling price of an article then
\[\text{Loss}=C.P-S.P\]
By using the above two formulas and the given selling prices we find the required cost price.
We are given that Praveen had the same amount of profit and loss for different selling prices.
We know that the cost price of the article doesn’t change in any condition.
Let us assume that the cost price of the article is \[C\]
Let us consider the profit condition of the given article.

Complete step by step answer:
We are given that he sold the article for Rs. 475 to get the profit
Let us assume that the selling price in this condition as
\[\Rightarrow {{S}_{1}}=475\]
We know that If C.P is the cost price and the S.P is the selling price of an article then
\[\text{Profit}=S.P-C.P\]
By using the above formula we get the profit of the article as
\[\begin{align}
  & \Rightarrow P={{S}_{1}}-C \\
 & \Rightarrow P=475-C \\
\end{align}\]
Now, let us consider the loss condition
We are given that if the selling price is Rs. 325 then he got the loss.
Let us assume that the selling price in this condition as
\[\Rightarrow {{S}_{1}}=475\]
We know that If C.P is the cost price and the S.P is the selling price of an article then
\[\text{Loss}=C.P-S.P\]
By using the above formula we get the profit of the article as
\[\begin{align}
  & \Rightarrow L=C-{{S}_{2}} \\
 & \Rightarrow L=C-325 \\
\end{align}\]
We are given that the profit and loss in the given two selling prices is same.
By converting the above statement into mathematical equation we get
\[\begin{align}
  & \Rightarrow P=L \\
 & \Rightarrow 475-C=C-325 \\
 & \Rightarrow 2C=800 \\
 & \Rightarrow C=400 \\
\end{align}\]
Therefore we can conclude that the cost price of given article is Rs. 400
So, option (a) is correct answer.


Note:
We have a direct condition for solving this problem.
If \[{{S}_{p}}\] is the selling price for getting profit, \[C\] is the cost price and \[{{S}_{l}}\] is the selling price for getting same loss as that of profit then \[{{S}_{p}},C,{{S}_{l}}\] will be in A.P.
We know that the standard condition that if \[a,b,c\] are in A.P then
\[\Rightarrow 2b=a+c\]
By using the above condition to given article then we get
\[\begin{align}
  & \Rightarrow 2C={{S}_{p}}+{{S}_{l}} \\
 & \Rightarrow 2C=475+325 \\
 & \Rightarrow C=\dfrac{800}{2}=400 \\
\end{align}\]
Therefore we can conclude that the cost price of given article is Rs. 400
So, option (a) is correct answer.