Question

a brother ask his sister for rs.100 so that he can be 3times as her sister, but the sister tells her brother to give her rs.400 , so that she can be 7 times as rich as her brother. how much money do the brother and sister have now?

Answer 1

sister = x
brother = y
$y + 100 = 3 x \\ \frac{y + 10}{3} = x......1 \\ x + 400 = 7y \\ x - 7y = - 400.......2$
substitute 1 in 2
$( \frac{y + 10}{3} ) - 7y = - 400$
multiply both sides with 3
$y + 10 - 21y = - 1200 \\ 10 - 20y = - 1200 \\ - 20y = - 1210 \\ y = \frac{121}{2} \\ y = 60.5$
substitute y=60.5 in 2

$x - 7(60.5) = - 400 \\ x - 423.5 = - 400 \\ x = - 400 + 423.5 \\ x = 23.5$