Question

A boat takes $4hr$ upstream and $2hr$ down the stream for covering the same distance. The ratio of velocity of boat to the water in river is

• A. $1:3$
• B. $3:1$
• C. $1:\sqrt{3}$
• D. $\sqrt{3}:1$

Answer 1

The correct option is B $3:1$

Let the speed of boat in still water be $x$ km/hr

speed of stream be $y$ km/hr

$\therefore$ The speed of the boat upstream $=(x-y)km/hr$

speed of the boat downstream $=(x+y)km/hr$

Given

Time taken to go upstream is $4$ hrs

Time taken to go downstream is $2$ hrs

We know that

$\frac{distance}{speed}=time$

Let the distnace covered by both the boats be $d$

Then, for upstream

$\frac{d}{x-y}=4$

$4x-4y=d.....\left(1\right)$

and for downstream

$\frac{d}{x+y}=2$

$2x+2y=d.....\left(2\right)$

Equating eq (1) and (2)

$4x-4y=2x+2y$

$2x=6y$

$x=3y$

$x:y=3:1$

Hence, the ratio of velocity of boat to the water or stream is $3:1$