Question

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 her brother. How much money do the brother and sister have now?

Answer 1

Let $x$ and $y$ be the money brother and sister have.

Now according to the question-

Condition I:-

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

$\Rightarrow x+100=3y-300$

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

Condition II:-

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

$\Rightarrow y+400=7x-2800$

$\Rightarrow y=7(3y-400)-3200\left(\text{From}\left(1\right)\right)$

$\Rightarrow y=21y-2800-3200$

$\Rightarrow 21y-y=6000$

$\Rightarrow y=\frac{6000}{20}=300$

Substituting the value of $y$ in equation $\left(1\right)$, we have

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

Hence the brother and sister have $Rs.500$ and $Rs.300$ respectively.