A man has divided his total money in his will in such a way that half of it goes to his wife, $\frac{2}{3}$rd of the remaining among his three sons equally and the rest among his four daughters equally. If each daughter gets ₹ 20,000, how much money will each son get?

## Concept & Logic This problem revolves around fraction distribution and successive remainders. By determining what fraction of the total estate corresponds to a single daughter's share, we can find the total estate or directly establish a ratio between a daughter's share and a son's share. $$ Fraction = \frac{Part}{Whole} $$ ## Step-by-Step Solution * **Calculation:** Let the total money be $x$. The wife receives $\frac{x}{2}$. * **Deduction:** The remaining money after the wife's share is $x - \frac{x}{2} = \frac{x}{2}$. * **Calculation:** The three sons share $\frac{2}{3}$ of this remainder. Total share of 3 sons = $\frac{2}{3} \times \frac{x}{2} = \frac{x}{3}$. Share of one son = $\frac{\frac{x}{3}}{3} = \frac{x}{9}$. * **Calculation:** The four daughters share the rest of the remainder. Total share of 4 daughters = $\frac{x}{2} - \frac{x}{3} = \frac{3x - 2x}{6} = \frac{x}{6}$. Share of one daughter = $\frac{\frac{x}{6}}{4} = \frac{x}{24}$. * **Substitution:** We are given that one daughter gets ₹ 20,000. $\frac{x}{24} = 20000 \implies x = 480,000$ (Total Money). * **Calculation:** We need the share of one son. Son's share = $\frac{x}{9} = \frac{480000}{9} = 53333.33$. ## Exam Strategy & Shortcut Bypass finding the total sum by comparing the fractions directly. One daughter gets $\frac{1}{24}$ of the total. One son gets $\frac{1}{9}$ of the total. Ratio of (One Son's Share) : (One Daughter's Share) = $\frac{1}{9} : \frac{1}{24} = 24 : 9 = 8 : 3$. Since 3 units = ₹ 20,000, then 1 unit = $\frac{20000}{3}$. The son gets 8 units = $8 \times (\frac{20000}{3}) = \frac{160000}{3} = 53333.33$. ## Common Pitfall Calculating the sons' share as $\frac{2}{3}$ of the *total* money instead of the *remaining* money. This leads to incorrect fractions and a completely wrong valuation of the estate. Always pay close attention to the word "remaining". ## Final Answer Therefore, the correct answer is **₹ 53,333.33**.