If we multiply a fraction by itself and divide the product by its reciprocal, the fraction thus obtained is $18 \frac{26}{27}$. The original fraction is
(a)$\frac{8}{27}$
(b)$1 \frac{1}{3}$
(c)$2 \frac{2}{3}$
(d)None of these
Answer
Answer (as printed): C
Explanation
Let the fraction be $\frac{a}{b}$. Then, $$\begin{aligned} \left(\frac{a}{b} \times \frac{a}{b}\right) \div \frac{b}{a}=\frac{512}{27} & \Leftrightarrow \frac{a}{b} \times \frac{a}{b} \times \frac{a}{b}=\frac{512}{27} \\ & \Leftrightarrow\left(\frac{a}{b}\right)^{3}=\left(\frac{8}{3}\right)^{3} \Leftrightarrow \frac{a}{b}=\frac{8}{3}=2 \frac{2}{3} . \end{aligned}$$
Explanation as extracted from the printed page; notation may be imperfect.