Question

Two-thirds of a positive number and $\frac{25}{216}$ of its reciprocal are equal. Then the number is ?

• A. $\frac{25}{144}$
• B. $\frac{5}{12}$
• C. $\frac{144}{25}$
• D. $\frac{12}{5}$

Answer 1

The correct option is B $\frac{5}{12}$

Let the number be ${}^{\prime }{n}^{\prime }$ Then,
$\frac{2}{3}\times n=\frac{25}{216}\times \frac{1}{n}$

$\Rightarrow n\times n=\frac{25}{216}÷\frac{2}{3}$ ....( by cross multiplying )
$\Rightarrow n^2=\frac{25}{216}\times \frac{3}{2}$

$\Rightarrow n^2=\frac{25}{144}$
$\Rightarrow n=\sqrt{\frac{25}{144}}=\frac{\sqrt{25}}{\sqrt{144}}=\frac{5}{12}$.
Hence, required number is $\frac{5}{12}$.