Ashok can row upstream at 8 km/h and downstream at 12 km/h. What is the speed of the stream (in km/h)?

Introduction / Context:
This is a straightforward boats and streams question where the effective upstream and downstream speeds are given. From these, we can directly calculate the speed of the stream and, if needed, the speed of the boat in still water.

Given Data / Assumptions:

• Upstream speed (against the current) = 8 km/h.
• Downstream speed (with the current) = 12 km/h.
• Let b be the speed of the boat in still water.
• Let s be the speed of the stream.
• Then upstream speed = b - s, downstream speed = b + s.

Concept / Approach:
When upstream and downstream speeds are known, we can find both the still water speed and the current speed by solving two simple linear equations. Adding the equations gives twice the boat speed; subtracting them gives twice the stream speed. This method is standard and very quick once memorised.

Step-by-Step Solution:
Step 1: Write the equations based on definitions: b - s = 8 and b + s = 12. Step 2: Add the two equations: (b - s) + (b + s) = 8 + 12. Step 3: Left side simplifies to 2b; right side gives 20, so 2b = 20 ⇒ b = 10 km/h. Step 4: Subtract the first equation from the second: (b + s) - (b - s) = 12 - 8. Step 5: Left side simplifies to 2s; right side is 4, so 2s = 4 ⇒ s = 2 km/h.

Verification / Alternative check:
With b = 10 km/h and s = 2 km/h, upstream speed should be b - s = 10 - 2 = 8 km/h, which matches the given upstream speed. Downstream speed should be b + s = 10 + 2 = 12 km/h, matching the given downstream speed. Therefore, the stream speed of 2 km/h is fully consistent with the problem data.

Why Other Options Are Wrong:
If the stream speed were 3, 4.5, 5 or 6 km/h, then the implied still water speed would not simultaneously satisfy both given effective speeds. For example, if s = 3 km/h, then b would have to be 11 km/h to get 8 km/h upstream, but b + s would then be 14 km/h, not 12 km/h. Only s = 2 km/h works correctly in both directions.

Common Pitfalls:
A typical mistake is to confuse which equation to add and which to subtract, sometimes leading to b = 2 or s = 10, which are clearly unreasonable. Another issue is to misinterpret the values as still water and stream speeds instead of effective speeds. Always remember that upstream is slower (b - s) and downstream is faster (b + s), and solve the pair of equations systematically.

Final Answer:
The speed of the stream is 2 km/h.