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?

Correct option is C

Given:

The boatman rows 2 km downstream in 10 minutes.

The boatman rows 12 km upstream in 2 hours.

We need to find the speed of the stream.

Formula Used:

Speed =$$\frac{\text{Distance}}{\text{Time}}$$​​

When rowing downstream, the effective speed is b + s (speed of the boat plus the speed of the stream).

When rowing upstream, the effective speed is b - s  (speed of the boat minus the speed of the stream).

Solution:

Time taken for 2 km downstream: 10 minutes $$= \frac{10}{60} = \frac{1}{6}$$ hours.

Speed downstream =$$\frac{2 \, \text{km}}{\frac{1}{6} \, \text{hours}} = 2 \times 6 = 12 \, \text{km/h}.$$

Time taken for 12 km upstream: 2 hours.​​

Speed upstream =$$\frac{12 \, \text{km}}{2 \, \text{hours}} = 6 \, \text{km/h}.$$​​

Speed downstream = b + s = 12 km/h

Speed upstream = b - s = 6 km/h

From b + s = 12 and b - s = 6, add the two equations:

(b + s) + (b - s) = 12 + 6

2b = 18

b = 9 km/h

Now, substitute b = 9 into b + s = 12:

9 + s = 12

s = 12 − 9 = 3 km/h

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