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1. Two-third of a positive number and $\frac{25}{216}$ of its reciprocal are equal, The number is :

A. $\frac{5}{12}$

B. $\frac{12}{5}$

C. $\frac{25}{144}$

D. $\frac{144}{25}$

Solution:

Let the number be x
Then,

\begin{aligned} \frac{2}{3} x = \frac{25}{216} \times \frac{1}{x} \\ \Leftrightarrow x^{2} = \frac{25}{216} \times \frac{3}{2} \\ \Leftrightarrow x^{2} = \frac{25}{144} \\ \Leftrightarrow x = \sqrt{\frac{25}{144}} \\ \Leftrightarrow x = \frac{5}{12} \end{aligned}

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