Question

A banker sells a land for Rs. $75$ lakhs and gains as much percent as the cost price of the land. Find the cost price of the land.

• A. Rs. $50$ lakhs
• B. Rs. $20$ lakhs
• C. Rs. $30$ lakhs
• D. Rs. $40$ lakhs

Answer 1

The correct option is A Rs. $50$ lakhs

Let the C.P. of the land be $x$
Gain $\%=x\%$
Gain $=x\%$ of $x=$ $\frac{x^2}{100}$
S.P. $=$ C.P. $+$ gain
S.P. $=75$ lakhs
Therefore, $x+\frac{x^2}{100}=75$
$100x+x^2=7500$
$x^2+100x-7500=0$
$(x+150)(x-50)=0$
$x=-150$ or $50.$
Price cannot be negative,
So, cost price of the land $=$ Rs. $50$ lakhs.