A motor boat goes 48 km downstream and comes back to the starting point in 16 hours. If the speed of the stream is 4 km/hr, then the speed of the motor boat in still water is :

8 km/hr

The correct answer is Option (2) → 8 km/hr

Downstream speed = $v+u$  [v = Speed of boat]

Upstream speed = $v-u$ [u = Speed of stream]

$t_{down}=\frac{48}{v+u},t_{up}=\frac{48}{v-u}$

and,

$t_{down}+t_{up}=16$

$∴\frac{48}{v+4}+\frac{48}{v-4}=16$

$⇒\frac{96}{v^2+16}=16$

$⇒v^2-6v-16=0$

$⇒(v-8)(v+2)$

∴ v = 8 km/hr [only positive]