Question

A banker sells a land for Rs. $56$ lakhs and gains as much percent as the cost price of the land. Find the cost price of the land.

• A. Rs. $10$ lakhs
• B. Rs. $20$ lakhs
• C. Rs. $30$ lakhs
• D. Rs. $40$ lakhs

Answer 1

The correct option is D Rs. $40$ 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. $=56$ lakhs
Therefore, $x+\frac{x^2}{100}=56$
$100x+x^2=5600$
$x^2+100x-5600=0$
$(x+140)(x-40)=0$
$x=-140$ or $40$
Price cannot be negative,
So, cost price of the land $=$ Rs. $40$ lakhs.