$X$ gives $\frac{1}{2}$ of his property to his wife and $\frac{1}{2}$ of the rest to his son. The remainder is divided equally between his two daughters. The share of each daughter is
(a)$\frac{1}{4}$
(b)$\frac{1}{6}$
(c)$\frac{1}{8}$
(d)$\frac{2}{3}$
Answer
Answer (as printed): C
Explanation
Let the whole property be worth ₹ $x$. Then, $$\begin{aligned} & \text { wife's share }=₹ \frac{x}{2} \text {; Son's share }=₹\left(\frac{1}{2} \text { of } \frac{x}{2}\right)=₹ \frac{x}{4} . \\ & \text { Remaining share }=₹\left[x-\left(\frac{x}{2}+\frac{x}{4}\right)\right]=₹ \frac{x}{4} . \\ & \therefore \quad \text { Share of each daughter }=₹\left(\frac{1}{2} \text { of } \frac{x}{4}\right)=₹ \frac{x}{8} . \end{aligned}$$
Explanation as extracted from the printed page; notation may be imperfect.