Question

A man can row at 5kmph in still water. If the velocity of current is 1 kmph and it takes him 1 hour to row to a place and come back, how far is the place?
A. 2.4km
B. 2.5km
C. 3km
D. 3.6km

Answer 1

Hint: We can do this question by calculating time in downstream direction and upstream direction in terms of unknown distance.

Complete step-by-step answer:
The distance of the place is x km.
Man’s velocity in still water is 5kmph and velocity of current is 1 kmph.
When man goes in a downstream direction in that case velocity of man will increase because we will add velocity of current in that case.
So velocity in downstream direction is $$5+1=6\text{ km/h}$$
When man goes in an upstream direction, in that case velocity of man will decrease because we will subtract velocity in this case.
So velocity in upstream direction is $$5-1=4\text{ km/h}$$
Total time to row a place and come back is 1 hr.
So we can write
$\Rightarrow {\displaystyle \frac{x}{6}}+{\displaystyle \frac{x}{4}}=1$
$\Rightarrow {\displaystyle \frac{4x+6x}{24}}=1$
$\Rightarrow {\displaystyle \frac{10x}{24}}=1$
$\Rightarrow x={\displaystyle \frac{24}{10}}$
$\Rightarrow x=2.4km$
Hence the place is 2.4km far.
Option A is correct.

Note: We need to be careful about the unit of distance. As velocity in kmph then distance will also be in km.
In general downstream in the river means, going with the direction of the river. So in this case we add velocity with velocity of river which we also know as velocity of current.
Similarly upstream in the river means going in the opposite direction of the river. So in this case we subtract velocity with velocity of river.