Five cities P, Q, R, S and T are connected by different modes of transport as follows: P and Q are connected by boat as well as rail. Sand R are connected by bus and boat. Q and T are connected by air only. P and R are connected by boat only. T and R are connected by rail and bus. 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?

The problem asks us to find which city must be visited twice when starting from P, visiting all other cities (Q, R, S, T), and returning to P. Let's list the connections: 1. P and Q are connected. 2. S and R are connected. 3. Q and T are connected. 4. P and R are connected. 5. T and R are connected. Now, let's look at the connections for each city: * P connects to Q and R. * Q connects to P and T. * R connects to S, P, and T. * S connects only to R. * T connects to Q and R. The key observation is for city S. City S is only connected to city R. This means that to visit S, you must travel from R to S. After visiting S, to continue the journey to any other city (or back to P), you must travel back from S to R, because R is the only city S is connected to. Therefore, any path that includes visiting S must contain the sequence R -> S -> R. This sequence forces R to be visited twice in the journey (once to enter S, and once to exit S). Let's illustrate with an example path: Start at P. 1. P -> Q (visited P, Q) 2. Q -> T (visited P, Q, T) 3. T -> R (visited P, Q, T, R) 4. R -> S (visited P, Q, T, R, S) Now all cities (P, Q, R, S, T) have been visited. We are at S and need to return to P. 5. S -> R (Since S only connects to R, we must go back to R. R is visited for the second time here.) 6. R -> P (Now at R, we can go back to P.) The complete path is P -> Q -> T -> R -> S -> R -> P. In this path, P is visited at the start and end. Q, T, S are visited once. R is visited twice. Since S only connects to R, the segment R-S-R is mandatory for any path that visits S and then continues to other parts of the graph. This means R must be visited twice. The final answer is B