A swimmer whose speed in swimming pool is 5 km/h, swims between two points in a river and returns back to starting point. He took 20 minutes more to cover the distance upstream than to cover downstream. If the speed of stream is 2 km/h, then the distance between two points is

1.75 km

The correct answer is Option (1) → 1.75 km

Swimmer speed in still water: $u = 5$ km/h

Speed of stream: $v = 2$ km/h

Time difference: $\Delta t = 20$ min $= \frac{1}{3}$ h

Distance between points: $d$ km

Speed downstream: $u+v = 5+2 = 7$ km/h

Speed upstream: $u-v = 5-2 = 3$ km/h

Time downstream: $t_1 = \frac{d}{7}$ h

Time upstream: $t_2 = \frac{d}{3}$ h

Given $t_2 - t_1 = \frac{1}{3}$:

$\frac{d}{3} - \frac{d}{7} = \frac{1}{3}$

$\frac{7d - 3d}{21} = \frac{1}{3}$

$\frac{4d}{21} = \frac{1}{3} \Rightarrow 4d = 7 \Rightarrow d = \frac{7}{4} = 1.75$ km