NIFT UG 2015 Question Paper with solutions

Let, speed of boat in still water is u km/h
downstream speed = (u + 5)
upstream speed = (u – 5)
Time to go from point
I to II, ${\mathit{t}}_1=\frac{\mathit{d}}{\left(\mathit{u}+5\right)}$
{Here, d = distance between two points}
II to I,${\mathit{t}}_2=\frac{\mathit{d}}{\left(\mathit{u}-5\right)}$
From question,
$\frac{{\mathit{t}}_1}{{\mathit{t}}_2}=\frac{3}{5}$
$\frac{\frac{\frac{\mathit{d}}{\left(\mathit{u}+5\right)}}{\mathit{d}}}{\left(\mathit{u}-5\right)}=\frac{3}{5}$
$\Rightarrow \frac{\left(\mathit{u}-5\right)}{\left(\mathit{u}+5\right)}=\frac{3}{5}$
$5\left(\mathit{u}\mathit{–}5\right)=3\left(\mathit{u}+5\right)$
$\therefore \mathit{u}=20$km/h