Question

A motor boat covers a certain distance downstream, in a river in $3$ hours. It covers the same distance upstream in $3$ hours and a half. If the speed of water is $1.5$ km/hr, then the speed of the boat in still water is:

• A. $17$ km/hr
• B. $19.5$ km/hr
• C. $17.5$ km/hr
• D. $19$ km/hr

Answer 1

The correct option is B $19.5$ km/hr

Let the speed of boat in still water be x km/hr and the distance be y km.
Speed in downstream = $(x+1.5)$ km/hr
Speed in upstream $(x-1.5)$ km/hr
According to the question,
$\frac{y}{x+1.5}$ = $3$ .................(1)
$\frac{y}{x-1.5}=\frac{7}{2}$.............(2)
On dividing equation (1) by (2),
$\frac{x-1.5}{x+1.5}=\frac{3\times 2}{7}=\frac{6}{7}$
$\Rightarrow 7x-10.5=6x+9\Rightarrow x=10.5+9=19.5km/hr$