Question : A clock was sold for Rs. 144. If the percentage of profit was numerically equal to the cost price, the cost of the clock was:
Option 1: Rs. 72
Option 2: Rs. 80
Option 3: Rs. 90
Option 4: Rs. 100
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Correct Answer: Rs. 80
Solution :
Here, SP is the selling price and CP is the cost price.
Given: SP of the clock = Rs. 144
Let CP = Profit % = $x$
According to the question,
Profit % = $\frac{\text{SP – CP}}{\text{CP}}$ × 100
$⇒x = \frac{144-x}{x} × 100$
$⇒x^2 = 14400 - 100x$
$⇒x^2 + 100x - 14400 = 0$
$⇒x^2 + 180x - 80x-14400 = 0$
$⇒x(x + 180) - 80(x + 180) = 0$
$⇒(x + 180)(x - 80) = 0$
$\therefore x = 80$
Hence, the correct answer is Rs. 80.
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