Question : Manoj bought two TVs for Rs. 2280. He sold one at a loss of 20% and the other at a profit of 10%. If each TV was sold for the same price, then what is the cost price of the TV that was sold at a loss?
Option 1: Rs. 1380
Option 2: Rs. 1320
Option 3: Rs. 1050
Option 4: Rs. 1440
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Correct Answer: Rs. 1320
Solution : Let the cost price of the TV sold at a loss as L and the cost price of the TV sold at a profit as P. Given that Manoj bought two TVs for Rs. 2280. $⇒L + P = 2280$ ____(1) He sold the first TV at a loss of 20%, so its selling price was $0.8L$. He sold the second TV at a profit of 10%, so its selling price was $1.1P$. Given that, each TV was sold for the same price. $⇒0.8L = 1.1P$ ____(2) From equation (2), $⇒P = \frac{0.8L}{1.1} = \frac{8L}{11}$ Substitute this into equation (1), $⇒L + \frac{8L}{11} = 2280$ $⇒11L + 8L = 2280 \times 11$ $⇒19L = 25080$ $⇒L = \frac{25080}{19} = 1320$ Hence, the correct answer is Rs. 1320.
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