Subject: General Aptitude · Chapter: Problems on Numbers · Exam: · Marks: · Difficulty:
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)$\frac{144}{25}$
Answer
Answer (as printed): A
Explanation
Let the number be $x$. Then, $\frac{2}{3} x=\frac{25}{216} \times \frac{1}{x} \Leftrightarrow x^{2}=\frac{25}{216} \times \frac{3}{2}$ $$=\frac{25}{144} \Leftrightarrow x=\sqrt{\frac{25}{144}}=\frac{5}{12} .$$
Explanation as extracted from the printed page; notation may be imperfect.