Question

The velocity of a swimmer in the direction of flow of river is \(10 \, \text{kmh}^{-1}\) and that against the flow of river is \(6 \, \text{kmh}^{-1}\). The velocity of the swimmer in still water in \(\text{kmh}^{-1}\) is

• A. 6
• B. 8
• C. 7
• D. 5
• E. 9

Hint:

Still water speed = \(\frac{\text{downstream} + \text{upstream}}{2}\).

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
Let \(v\) = velocity of swimmer in still water, \(u\) = velocity of river.
Downstream: \(v + u = 10\)
Upstream: \(v - u = 6\)

Step 2: Detailed Explanation:
Adding the two equations: \(2v = 16 \Rightarrow v = 8\) \(\text{kmh}^{-1}\)

Step 3: Final Answer:
Velocity in still water = 8 \(\text{kmh}^{-1}\).