Question

If the government wants to ensure that the traffic at S gets evenly distributed along streets from S to A, from S to B, and from S to D, then a feasible set of toll charged (in rupees) at junctions A, B, C and D respectively to achieve this goal is:

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

Answer 1

The correct option is A 0,5,4,1

Available paths considering no toll are
SAT $\to$ Rs. 14
SBAT $\to$ Rs. 7
SBCT $\to$ Rs. 9
SDCT $\to$ Rs. 10
SDT $\to$ Rs. 13
Fuel cost on Path SAT - fuel cost on SDT = 14 - 13 = Rs. 1, toll at junction D should be 1 more than the toll at junction A.
So, option (b) and (c) are ruled out
Checking options (a) and (d)
When A = 0, paths SAT, SBAT and SDT are equally likely to be taken by a motorist.
When A = 1, cost on SAT and SBAT are not equal.