A person can row \(22\frac{1}{2}\) km an hour in still water and he finds that it takes him twice as long to row up as to row down the stream. The speed of the stream is:

Given:

Speed in still water (u) = 22.5 km/hr

Time taken to row upstream = 2 × Time taken to row downstream

Formula used:

Speed downstream = (u + v) km/hr

Speed upstream = (u - v) km/hr

Where, v = speed of stream

Calculation:

Let the speed of stream be v km/hr.

Time taken to row downstream = d / (u + v)

Time taken to row upstream = d / (u - v)

Given, Time taken to row upstream = 2 × Time taken to row downstream

⇒ d / (u - v) = 2 × d / (u + v)

⇒ 1 / (u - v) = 2 / (u + v)

⇒ u + v = 2 × (u - v)

⇒ u + v = 2u - 2v

⇒ 3v = u

⇒ v = u / 3

Given, u = 22.5 km/hr

⇒ v = 22.5 / 3

⇒ v = 7.5 km/hr

∴ The correct answer is option 1.