Explanation:

- The boat travels downstream and its speed is the sum of its speed in still water and the stream's velocity: \(14 + 4 = 18\) kmph.

- Upstream, the boat's speed is reduced by the stream's velocity: \(14 - 4 = 10\) kmph.

- We know it takes 38 hours to go downstream from A to B and then upstream to C.

- Let the distance between A and B be \(x\) km. Distance A to C is \(1.5 \times x \) km.

- Time downstream (A to B) = \(x/18\) hours.

- Time upstream (B to C) = \((0.5 \times x)/10\) hours.

- The total time for the journey is \(x/18 + (0.5 \times x)/10 = 38\).

- Solving \(\frac{x}{18} + \frac{0.5x}{10} = 38\), we find the value of \(x\).

- Solving gives \(x = 360\) km.

Option 3: 360 km is the correct answer. .