Question

If the government wants to ensure that no traffic flows on the street from D to T, while equal amount of traffic flows through junctions A and C, then a feasible set of toll charged (in rupees) at junction A, B, C and D respectively to achieve this goal is:

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

Answer 1

The correct option is D 0,5,2,2

No traffic flows on the street from D and T. Now we have fuel cost on different paths as SAT 9+5 = Rs. 14 + toll at junction A
SBAT 2 + 2 + 5 = Rs. 9 + toll at junction B and A
SBCT 2 + 3 + 2 = Rs. 7 + toll at junction B and C
SDCT 7 + 1 + 2 = Rs. 10 + toll at junction D and C
Now checking the option we find that toll at junction A is 0 or 1.
When toll is 0, fuel cost on SAT = 14 + 0 = Rs. 14
When toll is 1, fuel cost on SAT = 14 + 1 = Rs. 15
The fuel cost on all the paths should be equal.
OptionS (a), (b), (c), can be ruled out as in all these options, tolls at C and D add up to more than Rs. 5. As fuel cost on SDCT is Rs. 10 without toll, so with toll, it cannot exceed Rs. 15 (i.e. toll of path SAT)
If option (d) taken, then fuel cost on all paths is Rs. 14.