Question

If the government wants to ensure that all routes from S to T get the same amount of traffic, then a feasible set of toll charged (in rupees) at junctions A, B, C and D respectively to achieve this goal is:

• A. 0,5,2,2
• B. 0,5,4,1
• C. 1,5,3,3
• D. 1,5,3,2

Answer 1

The correct option is D 1,5,3,2

Available routes are
SAT $\to$ Rs. 14
SBAT $\to$ Rs. 9
SBCT $\to$ Rs. 7
SDCT $\to$ Rs. 10
SDT $\to$ Rs. 13
Fuel cost on path SAT - fuel path SDT = 14 - 13 = Rs. 1
So, the toll at junction D should be 1 more than toll at junction A.
So, options (a) and (c) are ruled out.
Fuel cost on path SAT - fuel cost on path SBCT = 14 - 7 = Rs. 7
So, the sum of tolls at junction B and C should be 7 more than the toll at A. Hence only option (d) matches.