If a number is multiplied by two-third of itself the value so obtained is 864. What is the number ?

Answer: Option B

Let the number be x
Then,
$$\begin{array}{rl}& \iff x\times \frac{2}{3}x=864\\ & \iff \frac{2}{3}{x}^2=864\\ & \iff x^2=\left(\frac{864\times 3}{2}\right)\\ & \iff x^2=1296\\ & \iff x=\sqrt{1296}\\ & \iff x=36\end{array}$$