Question

A motor boat covers a certain distance downstream in 30 minutes, while it comes back in 45 minutes. If the speed of the stream is 5 kmph what is the speed of the boat in still water?

• A. 10 kmph
• B. 15 kmph
• C. 20 kmph
• D. 25 kmph

Answer 1

The Correct Option is D

1. Let the speed of the boat in still water be b kmph, and the speed of the stream is 5 kmph. 

2. Downstream speed (boat going with the stream):

Downstream speed = b + 5 kmph

3. Upstream speed (boat going against the stream):

Upstream speed = b - 5 kmph

4. Distance covered downstream and upstream is the same. Let the distance be D.

5. Time taken downstream:

• Time downstream = 30 minutes = 0.5 hours
• Using the formula Distance = Speed × Time: D = (b + 5) × 0.5

6. Time taken upstream:

• Time upstream = 45 minutes = 0.75 hours
• Using the formula Distance = Speed × Time: D = (b - 5) × 0.75

7. Set the two expressions for D equal to each other:

(b + 5) × 0.5 = (b - 5) × 0.75

8. Solve for b:

• 0.5b + 2.5 = 0.75b - 3.75
• 2.5 + 3.75 = 0.75b - 0.5b
• 6.25 = 0.25b
• b = 25 kmph

Final Answer: The speed of the boat in still water is 25 kmph.