A motor boat can travel at 12 km/hr in still water. It travelled 63 km downstream in river and then returned back taking altogether 24 hours. The speed of the water current in the river is:
Answer & explanation
Correct answer: option 2
$\text{Speed in still water}=12.$
$\text{Let speed of current}=v.$
$\text{Downstream speed}=12+v.$
$\text{Upstream speed}=12-v.$
$\frac{63}{12+v}+\frac{63}{12-v}=24.$
$\frac{63(12-v)+63(12+v)}{144-v^2}=24.$
$\frac{63(24)}{144-v^2}=24.$
$1512=24(144-v^2).$
$1512=3456-24v^2.$
$24v^2=1944.$
$v^2=81.$
$v=9.$
$\text{Speed of water current}=9\text{ km/hr}.$