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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