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

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

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