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

A. 34

B. 36

C. 38

D. 44

E. 46

Answer: Option B

Solution(By Examveda Team)

Let the number be x
Then,
$$\eqalign{ & \Leftrightarrow x \times \frac{2}{3}x = 864 \cr & \Leftrightarrow \frac{2}{3}{x^2} = 864 \cr & \Leftrightarrow {x^2} = \left( {\frac{{864 \times 3}}{2}} \right) \cr & \Leftrightarrow {x^2} = 1296 \cr & \Leftrightarrow x = \sqrt {1296} \cr & \Leftrightarrow x = 36 \cr} $$