If the organizers want to ensure that all routes from S to T get the same number of participants, then a feasible set of task time (in hours) at junctions A, B, C, and D respectively to achieve this goal is:
The correct option is D 1,5,3,2
The possible routes are -
RouteTotal TimeJunctionS−A−T14AS−B−A−T9A,BS−B−C−T7B,CS−D−C−T10C,DS−D−T13D
It is given that, for each of the routes, the only way to increase the total time is to impose task time at the junctions. Let the task time at A, B, C, D be a, b, c, d hours respectively.
Now, the total time for each of the five routes will be as follows.
RouteTotal TimeS−A−T14+aS−B−A−T9+(a+b)S−B−C−T7+(b+c)S−D−C−T10+(c+d)S−D−T13+d
From the given options, new times will be as follows -
RouteOption aOption bOption cOption dS−A−T14141515S−B−A−T14141515S−D−C−T14141515S−D−T15141615
Since the organizers want to ensure that all routes from S to T get the same number of participants, the time must be same for all the routes. So it must be option (d).
The possible routes are -
RouteTotal TimeJunctionS−A−T14AS−B−A−T9A,BS−B−C−T7B,CS−D−C−T10C,DS−D−T13D
It is given that, for each of the routes, the only way to increase the total time is to impose task time at the junctions. Let the task time at A, B, C, D be a, b, c, d hours respectively.
Now, the total time for each of the five routes will be as follows.
RouteTotal TimeS−A−T14+aS−B−A−T9+(a+b)S−B−C−T7+(b+c)S−D−C−T10+(c+d)S−D−T13+d
From the given options, new times will be as follows -
RouteOption aOption bOption cOption dS−A−T14141515S−B−A−T14141515S−D−C−T14141515S−D−T15141615
Since the organizers want to ensure that all routes from S to T get the same number of participants, the time must be same for all the routes. So it must be option (d).
