Question

A man on a boat goes 10 km upstream and comes back to the starting point in the same path in 55 minutes. If the speed of the stream is 2 kmph, then the speed of the boat in still water is:

• A. 25 kmph
• B. 27 kmph
• C. 22 kmph
• D. 30 kmph

Hint:

Total Time = $\frac{D}{v-s} + \frac{D}{v+s}$.

Answer 1

The Correct Option is C

Step 1: Concept
Upstream and Downstream motion.

Step 2: Analysis
Let boat speed = $v$. Upstream speed = $v-2$, Downstream speed = $v+2$.
Time = $10/(v-2) + 10/(v+2) = 55/60$ hours.

Step 3: Calculation
$10[(v+2 + v-2) / (v^2 - 4)] = 11/12$.
$20v / (v^2 - 4) = 11/12 \implies 240v = 11v^2 - 44$.
Solving $11v^2 - 240v - 44 = 0$ gives $v = 22$.

Step 4: Conclusion
The speed of the boat in still water is 22 kmph. Final Answer: (C)