B

To derive the correct options, we need to analyze the relationships between the velocities and the corresponding minimum distance and time scenarios.
Step 1: Analyze the velocity of the man relative to water, \( \bar{v}_{mw} \), and the velocity of the water, \( \bar{v}_{w} \).
Step 2: The angle \( \theta \) can be found using the formula:
\( \theta = \sin^{-1}\left(\frac{\bar{v}_{mw}}{\bar{v}_{w}}\right) \) where \( \bar{v}_{mw} > \bar{v}_{w} \) indicates that the man swims faster than the current.
Step 3: Minimum distance scenarios occur for various angles which correspond to getting directly to the point across the river.
The options can relate as follows:
- Minimum distance for II corresponds to the scenario where velocity across the width must be maximized.
- Minimum time for I occurs when the swimmer directly swims perpendicular to the water flow.
- This leads to matching: A - II, B - I, C - II, D - IV.
Final step: Therefore, the final correct matching is: A-III, B-I, C-II, D-IV. Hence, Option B is correct.