A boatman rows 2 km in 10 mins, along the stream and 12 km in 2 hours against the stream. What is the speed of the stream?

The correct option is 3 km/h.

Step 1: Find the speed along the stream (Downstream Speed)
Distance covered along the stream = 2 km
Time taken = 10 minutes = 10 / 60 hour = 1 / 6 hour

$\text{Downstream Speed (}u\text{)}=\frac{\text{Distance}}{\text{Time}}=\frac{2\text{km}}{\frac{1}{6}\text{h}}=2\times 6=12\text{km/h}$

Step 2: Find the speed against the stream (Upstream Speed)
Distance covered against the stream = 12 km
Time taken = 2 hours

$\text{Upstream Speed (}v\text{)}=\frac{\text{Distance}}{\text{Time}}=\frac{12\text{km}}{2\text{h}}=6\text{km/h}$

Step 3: Calculate the speed of the stream
The formula for the speed of the stream is:

$\text{Speed of the stream}=\frac{\text{Downstream Speed (}u\text{)}-\text{Upstream Speed (}v\text{)}}{2}$

Substitute the values into the formula:

$\text{Speed of the stream}=\frac{12\text{km/h}-6\text{km/h}}{2}=\frac{6\text{km/h}}{2}=3\text{km/h}$

Thus, the speed of the stream is 3 km/h.