Question

Velocity of man swimming along the flow of river is 10 km/h and against the flow is 6 km/h. Velocity of man in still water is

• A. \( 8 \, \text{km/h} \)
• B. \( 7 \, \text{km/h} \)
• C. \( 5 \, \text{km/h} \)
• D. \( 9 \, \text{km/h} \)

Hint:

When calculating the velocity in still water, use the relative velocities along and against the flow of the river.

Answer 1

The Correct Option is A

Let the velocity of the man in still water be \( v_m \) km/h and the velocity of the river flow be \( v_r \) km/h. We are given that: - Velocity of the man along the flow of the river is \( 10 \, \text{km/h} \), - Velocity of the man against the flow of the river is \( 6 \, \text{km/h} \). When the man swims along the flow, his effective velocity is the sum of his swimming speed and the river's speed: \[ v_m + v_r = 10 \, \text{km/h} \] When the man swims against the flow, his effective velocity is the difference between his swimming speed and the river's speed: \[ v_m - v_r = 6 \, \text{km/h} \] Now, we solve these two equations simultaneously: \[ v_m + v_r = 10 \quad \text{(1)} \] \[ v_m - v_r = 6 \quad \text{(2)} \] Adding equations (1) and (2): \[ (v_m + v_r) + (v_m - v_r) = 10 + 6 \] \[ 2v_m = 16 \] \[ v_m = 8 \, \text{km/h} \]
Thus, the velocity of the man in still water is \( 8 \, \text{km/h} \).