Question

One says, "Give me a hundred, friend! I shall then becomes twice as rich as you." The other replies, "If you give me ten, I shall be six times as rich as you." Tell me what is the amount of their respective capital?

Answer 1

Let the capital of two of them be $x$ and $y$ respectively $.$

$\therefore 100+x=2(y-100)⟶\left(i\right)\Rightarrow x-2y+300=0⟶\left(iii\right)$ {as one says}

$10+y=6(x-10)⟶\left(ii\right)\times 2\Rightarrow -12x+2y+140=0⟶\left(iv\right)$ {as other says}

On adding $\left(iii\right)$ and $\left(iv\right)$ $,$

$-11x+440=0$

$\Rightarrow x=40$

putting $x$ in $\left(iii\right)$

$40-2y+300=0$

$\Rightarrow y=170$

$\therefore$ Their capitals are $40$ and $170$ respectively $.$