Ravi's speed of rowing in still water is 6 km/hr. He rows between two points in a river and return to the same starting point. He took 30 minutes more to cover the distance upstream than downstream. If the speed of the stream is 3 km/ hr, then the distance between the two points is:

2.25 km

The correct answer is Option (2) → 2.25 km

Given:

Speed of Ravi in still water: $u = 6$ km/hr

Speed of stream: $v = 3$ km/hr

Time difference upstream and downstream: $\Delta t = 0.5$ hours

Speed downstream: $u+v = 6+3 = 9$ km/hr

Speed upstream: $u-v = 6-3 = 3$ km/hr

Let distance between points be $d$ km.

Time downstream: $t_d = \frac{d}{9}$

Time upstream: $t_u = \frac{d}{3}$

Given $t_u - t_d = 0.5$

$\frac{d}{3} - \frac{d}{9} = 0.5$

$\frac{3d - d}{9} = 0.5 \Rightarrow \frac{2d}{9} = 0.5$

$2d = 4.5 \Rightarrow d = 2.25$ km