A motorboat has still water speed 30 km/h. From Mumbai to Goa it takes 2 hours, and on the same day from Goa back to Mumbai it takes 4 hours. Assuming one leg is downstream and the other upstream, what is the stream speed?

Introduction / Context:
Given a fixed still water speed and different one way times on the same route, we infer that the shorter time corresponds to downstream and the longer to upstream. With equal distances, we can solve for the stream speed using effective speeds and travel times.

Given Data / Assumptions:

• Still water speed u = 30 km/h.
• Downstream time = 2 h; upstream time = 4 h.
• Let stream speed be v km/h; distance each way is D.

Concept / Approach:
Downstream speed = u + v = D / 2 and upstream speed = u - v = D / 4. Equate the distances to eliminate D and solve for v.

Step-by-Step Solution:

Verification / Alternative check:
Downstream speed = 40 km/h; upstream speed = 20 km/h. Distance D = 40 * 2 = 80 km. Upstream time = 80 / 20 = 4 h, consistent.

Why Other Options Are Wrong:
8.5, 11.5, and 12 km/h do not satisfy the relation 2(u + v) = 4(u - v) with u = 30 km/h.

Common Pitfalls:
Taking the average of times or speeds. The harmonic relation between speeds for equal distances must be honoured through equations.

Final Answer:
10 km/h