Here, instead of calculating the value for each and every route, consider the three cities directly connected to P i.e. Q, S and R. Consider one at a time, and connect that city to the next one and so on till V is reached. Consider only the shortest path. On each path, choose the cheaper mode of transport for that path.
If one goes from P to Q, the possible routes are P-Q-U-V and P-Q-T-V. Taking the cheapest mode of transport in each step of these two paths, the time is:
P-Q-U-V = P-Q + Q-U + U-V = 3 + 5 + 4 = 12 hours.
P-Q-T-V = P-Q + Q-T + T-V = 3 + 3 + 6 = 12 hours.
If one goes from P to S, the shortest path is P-S-V
So, P-S-V = P-S + S-V = 6 + 6 = 12 hours.
If one goes from P to R, the only possible path is P-R-T-V.
So, P-R-T-V = P-R + R-T + T-V = 2 + 3 + 6 = 11 hours.
Thus, the minimum time is 11 hours.
Hence, option A is the correct choice.