A motor boat can travel at 9 km/hr in still water. It travelled 65 km downstream in river and then returned back taking altogether 18 hours. The speed of the stream is:

4 km/hr

The correct answer is Option (3) → 4 km/hr

$\text{Speed in still water} = 9 \text{ km/hr},\;\; \text{stream} = v$

$\text{Downstream speed} = 9+v,\;\; \text{Upstream speed} = 9-v$

$\frac{65}{9+v} + \frac{65}{9-v} = 18$

$65\left(\frac{1}{9+v} + \frac{1}{9-v}\right)=18$

$65\left(\frac{18}{81 - v^2}\right)=18$

$\frac{1170}{81 - v^2}=18$

$1170 = 18(81 - v^2)$

$1170 = 1458 - 18v^2$

$18v^2 = 288$

$v^2 = 16 \Rightarrow v=4$

The speed of the stream is $4$ km/hr.