Question

If the organizers want to ensure that all participants travelling from S to T take the same time (travelling time and task time combined) regardless of the route they choose and the street from B to C is under repairs (and hence unusable), then a feasible set of task time (in hours) at junctions A, B, C, and D respectively to achieve this goal is:

• A. 2,5,3,2
• B. 0,5,3,1
• C. 1,5,3,2
• D. Both (b) and (c)

Answer 1

The correct option is D Both (b) and (c)


The possible routes are -

$\begin{array}{ccc}Route& TotalTime& Junction\\ S-A-T& 14& A\\ S-B-A-T& 9& A,B\\ S-B-C-T& 7& B,C\\ S-D-C-T& 10& C,D\\ S-D-T& 13& D\end{array}$

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.

$\begin{array}{cc}Route& TotalTime\\ S-A-T& 14+a\\ S-B-A-T& 9+(a+b)\\ S-B-C-T& 7+(b+c)\\ S-D-C-T& 10+(c+d)\\ S-D-T& 13+d\end{array}$

As B - C is unusable; S - B - C - T is not possible. From the remaining options, if we apply all of them:

$\begin{array}{ccccc}Route& Optiona& Optionb& Optionc& Optiond\\ S-A-T& 16& 14& 15& \\ S-B-A-T& 16& 14& 15& \\ S-D-C-T& 15& 14& 15& \\ S-D-T& 15& 14& 15& \end{array}$

Both option (b) and (c) are true, as in both the cases total time is same for each of the four routes.