A person can row a boat at the rate of 5 km/hour in still water. He takes thrice as much time in going 40 km upstream as in going 40 km downstream. Find the speed of the stream.

Options

A. 5.2 km/h
B. 2.5 km/h
C. 3 km/h
D. none of these

Answer

B

Explanation

Let the speed of the stream be v km/h.
Given that, a person rowing in still water = 5 km/h
The speed of a person rowing in downstream = (5+v)km/h
and the speed of a person has rowing in upstream = (5-v) km/h
Now, the person taken time to cover 40 km downstream,
`t_(1)=(40)/(5+v)h " " `[`:' `speed = `("distance")/("time")`]
and the person has taken time to cover 40 km upstream,
`t_(2)=(40)/(5-v)h`.
By condition, ` " " t_(2)=t_(1)xx3`
`rArr " " (40)/(5-v)=(40)/(5+v)xx3`
`rArr " " (1)/(5-v)=(3)/(5+v)`
`rArr "" 5+v=15-3v rArr 4v=10`
`:. " " v=(10)/(4)=2.5` km/h
Hence, the speed of the stream is 2.5 km/h.