A man has divided his total money in his will in such a way that half of it goes to his wife, $\frac{2}{3} \mathrm{rd}$ 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?
(a)₹ 48,233.33
(b)₹ 50,333.33
(c)₹ 53,333.33
(d)Data inadequate
(e)None of these
Answer
Answer (as printed): C
Explanation
Wife's share $=\frac{1}{2}$. Remaining part $=\left(1-\frac{1}{2}\right)=\frac{1}{2}$. Share of 3 sons $=\left(\frac{2}{3}\right.$ of $\left.\frac{1}{2}\right)=\frac{1}{3}$. Remaining part $$=\left(\frac{1}{2}-\frac{1}{3}\right)=\frac{1}{6} .$$ Each daughter's share $=\frac{1}{4} \times \frac{1}{6}=\frac{1}{24}$. Let the total money be ₹ $x$. Then, $\frac{1}{24} x=20000$ $$\begin{aligned} & \Leftrightarrow \quad x=20000 \times 24=480000 . \\ & \therefore \quad \text { Each son's share }=₹\left[\frac{1}{3} \times\left(\frac{1}{3} \times 480000\right)\right]=₹ 53,333.33 . \end{aligned}$$
Explanation as extracted from the printed page; notation may be imperfect.