Ramesh rows a fixed distance downstream in 6 hours and the same distance upstream in 9 hours. If his still-water speed is 12 km/h, find the speed of the stream.

Introduction / Context:
Different times for the same distance downstream and upstream reflect different effective speeds. Knowing the still-water speed allows direct solution for the current speed.

Given Data / Assumptions:

• Still-water speed b = 12 km/h.
• Downstream time Td = 6 h, upstream time Tu = 9 h for the same distance D.
• Downstream speed = b + c; upstream speed = b - c.

Concept / Approach:
Equate distances: (b + c) * Td = (b - c) * Tu. Solve for c.

Step-by-Step Solution:
(12 + c) * 6 = (12 - c) * 9 72 + 6c = 108 - 9c 15c = 36 ⇒ c = 36 / 15 = 2.4 km/h

Verification / Alternative check:
Downstream speed = 14.4 km/h; upstream speed = 9.6 km/h. For any D, D/14.4 divided by D/9.6 equals 2/3, matching 6 h vs 9 h.

Why Other Options Are Wrong:
2 or 3 km/h do not satisfy the exact time ratio with b = 12 km/h; data is sufficient, so 'Data inadequate' is incorrect.

Common Pitfalls:
Adding times or averaging times; assuming average of speeds rather than solving the linear equation from equal distances.

Final Answer:
2.4 km/hr