David can row a boat in still water at the rate of 5 km/hr. He rowed in a river downstream to meet his friend. After returning back he observed that the duration of the upstream journey was three times that of the downstream journey. The speed of the stream was:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 2.5 km/hr
Let the speed of the stream be s km/hr. Then
\(\text{downstream speed} = 5 + s\)
\(\text{upstream speed} = 5 - s\)
The distance is the same both ways, so the times are in the inverse ratio of the speeds. The upstream time is three times the downstream time, so the downstream speed is three times the upstream speed:
\(5 + s = 3(5 - s)\)
\(5 + s = 15 - 3s\)
\(4s = 10,\quad s = 2.5\)
So the speed of the stream is 2.5 km/hr.
CBSE Applied Mathematics (Class XII):
Boats and Streams
