If a person visits each of the places starting from P and gets back to P, which of the following places must he visit twice?

Correct Option (B)

: R

For a complete traversal of all places, starting from P and returning to P, R must be visited twice. This is due to the specific network topology where a path exists from R to S, and S has no other outgoing paths that facilitate progression to other unvisited nodes or a direct return to P. Consequently, to visit S and then proceed with the journey, one must first traverse through R to reach S (e.g., ... → R → S). Subsequently, to exit S and continue the path towards P, a return traversal through R is necessary (S → R → ...). This sequence mandates two visits to R.

Incorrect Options:

Options Q, S, and T do not possess the network characteristic that would necessitate a double visit. Their positions within the network allow for a single traversal as part of the overall path, without requiring a revisit to enable access to other nodes or to complete the circuit back to P.