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A brother asks his sister for Rs100 so that he can be 3 times as rich as her sister, but the sister

tells her brother to give her Rs400, so that she can be 7 times as rich as his brother.The money now brother has and sister has .

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Detailed Solution

Concept: Let x and y be the money brother and sister have.
Now according to the question-
Condition I:-

x + 100 = 3 \times (y - 100)

\Rightarrow x + 100 = 3 y - 300

\Rightarrow x = 3 y - 400 . . . . . (1)

Condition II:-

y + 400 = 7 \times (x - 400)

\Rightarrow y + 400 = 7 x - 2800

\Rightarrow y = 7 (3 y - 400) - 3200

(From (1))

\Rightarrow y = 21 y - 2800 - 3200

\Rightarrow 21 y - y = 6000

\Rightarrow

y= 300
Substituting the value of y in equation (1), we have

x = 3 \times 300 - 400 = 900 - 400 = 500

Hence, the brothers and sisters are Rs.500 and Rs.300, respectively.

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