Question

The ratio of the speed of a boat in still water to the speed of the stream is 5:2. If the boat goes 14 km downstream in the same time as it goes 6 km upstream, the speed of the boat in still water is:

• A. 7 km/h
• B. 10 km/h
• C. 14 km/h
• D. 18 km/h

Hint:

In boat problems, always express speeds using ratios first—it simplifies equations significantly.

Answer 1

The Correct Option is B

Step 1: Assume speeds using ratio.
Let speed of boat in still water = \( 5x \) km/h
Speed of stream = \( 2x \) km/h
Step 2: Write downstream and upstream speeds.
Downstream speed = \( 5x + 2x = 7x \) km/h
Upstream speed = \( 5x - 2x = 3x \) km/h
Step 3: Use given distance-time condition.
According to the question:
\[ \frac{14}{7x} = \frac{6}{3x} \]
Step 4: Solve the equation.
\[ \frac{14}{7x} = \frac{6}{3x} \Rightarrow 2 = 2 \]
This confirms consistency of ratio.
Choosing \( x = 2 \):
\[ 5x = 10 \text{ km/h} \]
Step 5: Conclusion.
The speed of the boat in still water is 10 km/h.