Question : A shopkeeper sells an article at $13 \frac{1}{2}\%$ loss. If he sells it for INR 1,274 more, then he gains $11\%$. What is the cost price of the article?
Option 1: INR 4,874
Option 2: INR 4,800
Option 3: INR 5,200
Option 4: INR 5,274
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Correct Answer: INR 5,200
Solution :
Let the cost price be INR $x$.
Selling price at a $13 \frac{1}{2}\%$ loss $=(\frac{100-\frac{27}{2}}{100})x=\frac{173x}{200}$
According to the question,
$\frac{173x}{200}+1274=\frac{100+11}{100}x$
$⇒\frac{111x}{100}-\frac{173x}{200}=1274$
$⇒\frac{49x}{200}=1274$
$\therefore x =5200$
Hence, the correct answer is INR 5,200.
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