Question

A shopkeeper sells an article at a loss of $ 12\dfrac{1}{2}\% $ . Had he sold it for $ Rs.51.80 $ more, then he would have earned a profit of $ 6\% $ . The cost price of the article is:
A. $ Rs.280 $
B. $ Rs.250 $
C. $ Rs.380 $
D. $ Rs.240 $

Answer 1

Hint: Here, we are given the percentage values of profit and loss. First, we will assume the cost price (CP) as a variable and then find the selling price (SP) in terms of the same variable when there is a loss of $ 12\dfrac{1}{2}\% $ . Then we will again find the selling price for the profit of $ 6\% $ . As the difference in both the selling price is given in the question which is $ Rs.51.80 $ , we can determine the value of the assumed variable which will be the cost price of the article.

Complete step-by-step answer:
Let us take the cost price of the article CP as $ Rs.x $ .
It is given that the shopkeeper sells this article at a loss of $ 12\dfrac{1}{2}\% $ .
We know that selling price is given by
 $ SP = CP - loss $
 $ \Rightarrow SP = \left( {100 - 12\dfrac{1}{2}} \right)\% $ of $ x $
 $ \Rightarrow SP = \dfrac{{175}}{2}\% $ of $ x $
Now, it is given that if he sold it for $ Rs.51.80 $ more then he would have earned a profit of $ 6\% $ . Let the selling price for this case be $ SP' $ .
 $ SP' = CP + profit $
 $ \Rightarrow SP = \left( {100 + 6} \right)\% $ of $ x $
 $ \Rightarrow SP = 106\% $ of $ x $
The difference between these two selling prices is $ Rs.51.80 $ .
 $ \Rightarrow SP' - SP = 51.80 $
 $ \Rightarrow \left( {106 - \dfrac{{175}}{2}} \right)\% $ of $ x $ $ = 51.80 $
 $ \Rightarrow \dfrac{{37}}{2}\% $ of $ x $ $ = 51.80 $
 $ \Rightarrow x = \dfrac{{51.80 \times 100 \times 2}}{{37}} $
 $ \Rightarrow x = 280 $
Thus, the cost price of the article is $ Rs.280 $ .
So, the correct answer is “Option A”.

Note: In this problem, we have determined the selling price in terms of variable $ x $ of the article for both the cases. Then, by using the difference given in the question we have determined the value of cost price. Here, we should be careful while finding the value of $ x $ because all the values are in percentage and therefore at the end, we must multiply by 100 to obtain the required cost price.