Question

Divide Rs 1100 among A, B, C so that A shall receive $\frac{3}{7}$ of what B and C together receive and B may receive $\frac{2}{9}$ of what A and C receive.

Answer 1

$\begin{array}{c}Giventhatx+y+z=\mathrm{1100........}\left(1\right)\\ Alsogiventhat,\\ x=\frac{3}{7}\left(y+z\right)\\ y+z=\frac{7x}{3}\\ U\sin g\left(1\right),wegetx+\frac{7x}{3}=1100\\ \Rightarrow \frac{10x}{3}=1100\\ x=\frac{1100\times 3}{10}=Rs.330\\ Giventhat,y=\frac{2}{9}\left(x+z\right)\\ \Rightarrow x+z=\frac{9y}{2}\\ U\sin g\left(1\right)weget,y+\frac{9y}{2}=1100\\ \Rightarrow \frac{11y}{2}=1100\\ \therefore y=Rs.200\\ now,u\sin g\left(1\right)\\ Weget330+200+z=1100\\ \Rightarrow 530+z=1100\\ \therefore z=1100-530=570\end{array}$