The correct answer is: A. Profound : Depth
A circuitous route is a long and winding one. Profound depth is great depth. In both cases, the first word describes the second word in terms of its extent or degree.
The other options do not have the same relationship. Judicious selection is a careful choice. Devious argument is a dishonest or misleading argument. Problematic solution is a solution that is difficult or challenging.