Question : A shopkeeper purchases two items for Rs. 520. One is sold gaining 16% and the other at a loss of 10%, thus making no profit or loss. What is the selling price of the item sold at a loss?
Option 1: Rs. 288
Option 2: Rs. 232
Option 3: Rs. 320
Option 4: Rs. 200
Correct Answer: Rs. 288
Solution :
Given that, the cost price of two articles = Rs. 520
Suppose the cost price of the article sold at a loss = Rs. $y$
$\therefore$ cost price of the article sold at profit = Rs. (520 – $y$)
According to the question,
$y\times\frac{10}{100}=(520-y)\times\frac{16}{100}$
⇒ $5y = (520- y)\times 8$
⇒ $5y=4160-8y$
⇒ $13y = 4160$
$\therefore y=320$
Now, On a 10% loss,
$\therefore$ The selling price = $\frac{320\times90}{100}$ = Rs. 288
Hence, the correct answer is Rs. 288.
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