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

### Concept & Logic This is a sequential fraction problem. To avoid complex fractions, model the total property as a variable (like 1 or $x$) and deduct shares step-by-step from the remaining balance. ### Step-by-Step Solution * **Given:** Let the total property be 1 whole unit. * **Step 1:** Wife's share. $$\text{Wife gets } \frac{1}{2}$$ $$\text{Remaining property} = 1 - \frac{1}{2} = \frac{1}{2}$$ * **Step 2:** Son's share. He gets $\frac{1}{2}$ of the *rest*. $$\text{Son gets } \frac{1}{2} \times \left(\frac{1}{2}\right) = \frac{1}{4}$$ $$\text{New Remainder} = \text{Previous Remainder} - \text{Son's Share}$$ $$\text{New Remainder} = \frac{1}{2} - \frac{1}{4} = \frac{1}{4}$$ * **Step 3:** Daughters' share. The final remainder is divided equally between 2 daughters. $$\text{Each Daughter gets } = \frac{\frac{1}{4}}{2} = \frac{1}{4} \times \frac{1}{2} = \frac{1}{8}$$ ### Exam Strategy & Shortcut Assume a convenient number for the total property. Since you have to take half of it, and then half again, and then divide by 2, choose a number divisible by 8. Let total property = $₹ 8$. Wife gets $1/2$ of 8 = $₹ 4$. Remaining = $₹ 4$. Son gets $1/2$ of 4 = $₹ 2$. Remaining = $₹ 2$. Two daughters split $₹ 2$, so each gets $₹ 1$. Fraction = $1 / 8$. This mental model eliminates fraction arithmetic entirely. ### Common Pitfall The most common error is ignoring the phrase "of the rest". Students might assume the son gets $1/2$ of the *total* property, leaving 0 for the daughters. Always apply sequential fractions to the *new balance*. ### Final Answer Therefore, the correct answer is **$\frac{1}{8}$**.