A man 14

A man gave 1/3 of his wealth to his wife, 2/3 of the remaining to his daughter, and divided the remaining between his two sons equally. If the daughter received Rs 3000000 more than one of the sons, find the value of the father's property.

Final Answer:

x =  9000000 Rs

Step-by-step explanation:

$$\begin{gathered} r_1=\frac{1}{3}\doteq 0.3333 \\ {r}_2=\frac{2}{3}\cdot (1-r_1)=\frac{2}{3}\cdot (1-\frac{1}{3})=\frac{4}{9}\doteq 0.4444 \\ {r}_1\cdot x+r_2\cdot x+2\cdot s=x \\ {r}_2\cdot x=3000000+s \\ \frac{1}{3}\cdot x+\frac{4}{9}\cdot x+2\cdot s=x \\ \frac{4}{9}\cdot x=3000000+s \\ 3\cdot x+4\cdot x+9\cdot 2\cdot s=9\cdot x \\ 4\cdot x=9\cdot (3000000+s) \\ 18s-2x=0 \\ 9s-4x=-27000000 \\ Row2-\frac{9}{18}\cdot Row1\to Row2 \\ -3x=-27000000 \\ x=\frac{-27000000}{-3}=9000000=9000000\text{Rs} \\ s=\frac{0+2x}{18}=\frac{0+2\cdot 9000000}{18}=1000000 \\ s=1000000 \\ x=9000000 \\ \text{ Verifying Solution: } \\ w=r_1\cdot x=\frac{1}{3}\cdot 9000000=\frac{1\cdot 9000000}{3}=\frac{9000000}{3}=3000000\text{Rs} \\ d=r_2\cdot x=\frac{4}{9}\cdot 9000000=\frac{4\cdot 9000000}{9}=\frac{36000000}{9}=4000000\text{Rs} \\ {s}_1=(x-w-d)/2=(9000000-3000000-4000000)/2=1000000\text{Rs} \end{gathered}$$

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