Question

A person can swim in still water at 5 m/s. He moves In a river of velocity 3 m/s, first down the stream and next same distance up the stream. The ratio of times taken are.

• A. 1:1
• B. 1:2
• C. 1:4
• D. 4:1

Answer 1

The Correct Option is C

Given:
Swimming speed of the person in still water: \(v_{swim} = 5\)m/s.
Velocity of the river: \(v_{river} = 3\)m/s.

Downstream:
Speed relative to the ground: \(v_{\text{downstream}} = v_{\text{swim}} + v_{\text{river}} = 5 \text{ m/s} + 3 \text{ m/s} = 8 \text{ m/s}\).

Upstream:
Speed relative to the ground: \(v_{\text{upstream}} = v_{\text{swim}} - v_{\text{river}} = 5 \text{ m/s} - 3 \text{ m/s} = 2 \text{ m/s}\).

Time Ratio:
Let \(t_{down}\) be the time taken downstream and \(t_{up}\) be the time taken upstream.
Since distance is constant,
\(v_{\text{downstream}} \times t_{\text{down}} = v_{\text{upstream}} \times t_{\text{up}}\)
\(8 \times t_{down} = 2 \times t_{up}\)

\(\frac{t_{down}}{t_{up}} = \frac{2}{8} = \frac{1}{4}\)

So, the correct option is (C): 1:4.