# Section-1: Critical Path Solved QuestionLogical Reasoning Discussion

Common Information

There are seven cities P, Q, R, S, T, U, and V. The table below shows all the possible direct routes to and fro between any two of the cities. It also gives both the Air as well as the Land route distances (in miles) between those cities and the time required (in hrs) for the respective journeys. A person on any one of the above seven places can travel to any one of the remaining 6 places using Air or Land route only. The person can change his/her mode of transport (Air/Land) at any of the above seven places.

Table below can be scrolled horizontally

Direct
Routes
Air Distance
(in miles)
Air Time
(in hrs)
Land Distance
(in miles)
Land Time
(in hrs)
P – Q 1100 3 900 6
P – S 2200 6 2400 10
P – R 700 2 1000 6
Q – U 1800 5 2200 11
Q – T 800 3 1100 6
R – T 1000 3 1400 10
S – T 800 3 1000 5
S – V 2200 6 2800 14
T – V 2200 6 3000 15
U – V 800 4 1200 6
 Q. Common Information Question: 1/4 What is the minimum time required to travel from P to V?
 ✔ A. 11 hrs ✖ B. 13 hrs ✖ C. 10 hrs ✖ D. 14 hrs ✖ E. 12 hrs

Solution:
Option(A) is correct

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.