Two-third of a positive number and 25/216 of its reciprocal are equal, The number is :

Answer: Option A

Let the number be x
Then,
$$\begin{array}{rl}& \frac{2}{3}x=\frac{25}{216}\times \frac{1}{x}\\ & \iff x^2=\frac{25}{216}\times \frac{3}{2}\\ & \iff x^2=\frac{25}{144}\\ & \iff x=\sqrt{\frac{25}{144}}\\ & \iff x=\frac{5}{12}\end{array}$$