While selling a flowerpot for Rs. 96,the prof | vedclass

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Question

(D) Let the cost price of the flowerpot be $x$ rupees.
Given that the profit percentage is equal to the cost price,the profit percentage is $x\%$.
P

Vedclass · Accepted Answer

$60$

Vedclass · Answer

(D) Let the cost price of the flowerpot be $x$ rupees.
Given that the profit percentage is equal to the cost price,the profit percentage is $x\%$.
Profit = $\frac{x}{100} 	imes x = \frac{x^2}{100}$.
Selling Price = Cost Price + Profit = $x + \frac{x^2}{100}$.
Given that the selling price is Rs. $96$,we have the equation: $x + \frac{x^2}{100} = 96$.
Multiplying the entire equation by $100$,we get $100x + x^2 = 9600$.
Rearranging into a standard quadratic equation: $x^2 + 100x - 9600 = 0$.
Factoring the quadratic equation: $x^2 + 160x - 60x - 9600 = 0$.
$x(x + 160) - 60(x + 160) = 0$.
$(x - 60)(x + 160) = 0$.
This gives $x = 60$ or $x = -160$.
Since the cost price cannot be negative,the cost price is Rs. $60$.

While selling a flowerpot for Rs. $96$,the profit percentage is equal to its cost price in rupees. Find the cost price of the flowerpot.

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