The correct answer is option (B):
2 kmph
Here's how to solve this problem, broken down step-by-step:
1. Understand the Concepts:
* Downstream: When a boat travels downstream, it moves with the current of the stream, increasing its speed.
* Upstream: When a boat travels upstream, it moves against the current, decreasing its speed.
* Relative Speeds: Downstream speed is the boat's speed plus the stream's speed. Upstream speed is the boat's speed minus the stream's speed.
* Ratio: A ratio like 3:1 means that for every 3 parts of the boat's speed, the stream's speed is 1 part.
2. Calculate the Downstream Speed:
* Distance = 24 km
* Time = 3 hours
* Downstream Speed = Distance / Time = 24 km / 3 hours = 8 kmph
3. Set up Variables Based on the Ratio:
* Let the boat's speed be 3x kmph
* Let the stream's speed be x kmph
4. Relate the Downstream Speed to the Variables:
* Downstream Speed = Boat's Speed + Stream's Speed
* 8 kmph = 3x + x
* 8 = 4x
5. Solve for x (the stream's speed):
* x = 8 / 4
* x = 2 kmph
Therefore, the speed of the stream is 2 kmph.