Question

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

• 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 x Given $\frac{2}{3}x=\frac{25}{216}\times \frac{1}{x}$
$\Rightarrow x^2=\frac{25}{{216}_{72}}\times \frac{3^1}{2}=\frac{25}{144}$
$\Rightarrow x=\sqrt{\frac{25}{144}}=\frac{5}{12}$