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Two-third of a positive number and $$\frac{25}{216}$$ of its reciprocal are equal, The number is :
Answer & Solution
Correct Answer:
Option
A
Let the number be x
Then,
$$\eqalign{ & \frac{2}{3}x = \frac{25}{216} \times \frac{1}{x} \cr & \Leftrightarrow {x^2} = \frac{{25}}{{216}} \times \frac{3}{2} \cr & \Leftrightarrow {x^2} = \frac{{25}}{{144}} \cr & \Leftrightarrow x = \sqrt {\frac{{25}}{{144}}} \cr & \Leftrightarrow x = \frac{5}{{12}} \cr} $$
Then,
$$\eqalign{ & \frac{2}{3}x = \frac{25}{216} \times \frac{1}{x} \cr & \Leftrightarrow {x^2} = \frac{{25}}{{216}} \times \frac{3}{2} \cr & \Leftrightarrow {x^2} = \frac{{25}}{{144}} \cr & \Leftrightarrow x = \sqrt {\frac{{25}}{{144}}} \cr & \Leftrightarrow x = \frac{5}{{12}} \cr} $$
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