Question

A tradesman finds that by selling a bicycle for Rs. 75, which he had bought for Rs. $x$, he gained $x$%. Find the value of $x$.

• A. $20$
• B. $35$
• C. $50$
• D. $75$

Answer 1

The correct option is C $50$

Given : S.P = Rs. $75$, C.P = Rs. $x$ and Profit = $x$%

$\text{Profit (Rs.)}$ = $\frac{\text{P}rofit}{100}\times C.P$ and $\text{Profit (Rs.) = S.P - C.P}$

Profit (Rs.) = Rs.$(75-x)$ ...(1)

$\therefore$ Profit (Rs.) =$\frac{x}{100}\times x$ ..(2)

From eq(1) and eq.(2) we get

$75-x=\frac{x^2}{100}$

$x^2+100x-7500=0$

$x=\frac{-100\pm \sqrt{10000+30000}}{2}$

$x=\frac{-100\pm 200}{2}$
$x=50,-150$
Hence, $x=50$