Question : A person bought two goods for INR 19,500. He sold one at a loss of 20% and the other at a profit of 15%. If the selling price of each good is the same, find the cost price of goods sold at profit.
Option 1: INR 11,475
Option 2: INR 9,750
Option 3: INR 11,500
Option 4: INR 8,000
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Correct Answer: INR 8,000
Solution :
Let the cost price of the good sold with 20% loss be INR $x$.
Then, the cost price of the goods sold with 15% profit $=19500-x$
According to the question,
$\therefore x×\frac{100-20}{100}=(19500-x)×\frac{115}{100}$
⇒ $80x=2242500-115x$
⇒ $195x=2242500$
⇒ $x=\frac{2242500}{195}=11500$
So, the cost price of the goods sold with 15% profit $=19500-11500=8000$
Hence, the correct answer is INR 8000.
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