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.

Correct answer:

x = 9000000 Rs

Step-by-step explanation:

r_{1} = \frac{1}{3} ≐ 0.3333 r_{2} = \frac{2}{3} \cdot (1 - r_{1}) = \frac{2}{3} \cdot (1 - \frac{1}{3}) = \frac{4}{9} ≐ 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) 18 s - 2 x = 0 9 s - 4 x = - 27000000 R o w 2 - \frac{9}{1 8} \cdot R o w 1 \to R o w 2 18 s - 2 x = 0 - 3 x = - 27000000 x = \frac{- 2 7 0 0 0 0 0 0}{- 3} = 9000000 = 9000000 Rs s = \frac{0 + 2 x}{1 8} = \frac{0 + 2 \cdot 9 0 0 0 0 0 0}{1 8} = 1000000 s = 1000000 x = 9000000 Verifying Solution: w = r_{1} \cdot x = \frac{1}{3} \cdot 9000000 = \frac{1 \cdot 9 0 0 0 0 0 0}{3} = \frac{9 0 0 0 0 0 0}{3} = 3000000 Rs d = r_{2} \cdot x = \frac{4}{9} \cdot 9000000 = \frac{4 \cdot 9 0 0 0 0 0 0}{9} = \frac{3 6 0 0 0 0 0 0}{9} = 4000000 Rs s_{1} = (x - w - d) / 2 = (9000000 - 3000000 - 4000000) / 2 = 1000000 Rs

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