Question

The ratio between the speed of a boat and a stream is 3 : 1 respectively. If the boat covers 24 km in 3 hours downstream, what is the speed of the stream?

• A. 1.5 kmph
• B. 2 kmph
• C. 3 kmph
• D. 4 kmph
• E. 6 kmph

Answer 1

The Correct Option is B

Step 1: Understand the problem.
The ratio between the speed of the boat and the speed of the stream is given as 3:1. The boat covers 24 km in 3 hours downstream. We are asked to find the speed of the stream.

Step 2: Define the speeds of the boat and the stream.
Let the speed of the boat be \( 3x \) km/h and the speed of the stream be \( x \) km/h, as per the given ratio of 3:1.

Step 3: Use the downstream speed formula.
The downstream speed is the sum of the speed of the boat and the speed of the stream, i.e., \( (3x + x) = 4x \) km/h.
The boat covers 24 km downstream in 3 hours, so the downstream speed is: \[ \text{Downstream Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{24}{3} = 8 \, \text{km/h} \] Therefore, we have the equation: \[ 4x = 8 \] Solving for \( x \): \[ x = \frac{8}{4} = 2 \]

Step 4: Conclusion.
The speed of the stream is \( x = 2 \) km/h.

Final Answer:
The correct option is (B): 2 km/h.