Question

Arun's swimming speed in still water is 5 km/hr. He swims between two points in a river and returns to the starting point. He took 20 minutes more upstream than downstream. If the stream speed is 2 km/hr, the distance between the points is:

• A. 3 km
• B. 1.5 km
• C. 1.75 km
• D. 1 km

Answer 1

The Correct Option is C

We are given:

Speed in still water \(v = 5 \text{ km/hr}\),
Speed of stream \(u = 2 \text{ km/hr}\),
Additional time taken upstream = 20 minutes = \(\frac{1}{3}\) hours.

The effective speeds are:

Speed Upstream = \(v - u = 5 - 2 = 3 \text{ km/hr}\),
Speed Downstream = \(v + u = 5 + 2 = 7 \text{ km/hr}\).

Let the distance between the two points be \(d \text{ km}\). The time taken for upstream and downstream travel is:

Time Upstream = \(\frac{d}{3}\),
Time Downstream = \(\frac{d}{7}\).

The difference in time between upstream and downstream travel is:

\(\frac{d}{3} - \frac{d}{7} = \frac{1}{3}\).

Simplify the equation:

\(\frac{7d - 3d}{21} = \frac{1}{3}\),
\(\frac{4d}{21} = \frac{1}{3}\).

Multiply through by 21:

\(4d = 7\), \(d = \frac{7}{4} = 1.75 \text{ km}\).

Thus, the distance between the two points is 1.75 km.