Indian Institute of Foreign Trade 2008 Solved Paper

Let us assume the upstream speed of the boat = u and the downstream speed = v
$\frac{30}{\mathit{u}}+\frac{44}{\mathit{v}}=10$
$\frac{40}{\mathit{u}}+\frac{55}{\mathit{v}}=13$
Consider 1/u=a, 1/v=b, these equations become
$30\mathit{a}+44\mathit{b}=10$
$40\mathit{a}+55\mathit{b}=13$
We get a=1/5 and b=1/11 Hence, $\frac{1}{\mathit{u}}=\frac{1}{5}$ and $\frac{1}{\mathit{v}}=\frac{1}{11}=>\mathit{u}=5$ and $\mathit{v}=11$
Assuming speed of boat in still water is x and the speed of stream$=\mathit{y}$
$\mathit{u}=\mathit{x}-\mathit{y}=5$
$\mathit{v}=\mathit{x}+\mathit{y}=11$
From these equations, we get x=8 km/hr