Traffic Flow and Toll Charges
CAT 2006 Slot 1 · DILR · Hard · Data Interpretation
Passage / data set
Traffic flows from point S to point T in a one-way street network with junctions A, B, C, D. Fuel costs in Rupees along streets:
- S-A: 9, S-B: 2, S-D: 7
- B-A: 2, B-C: 3, B-D: 1 (wait, arrow B to C cost 3, B to A cost 2, D to C cost 1)
- A-T: 5, C-T: 2, D-T: 6
Motorists take the route(s) with minimum total cost (fuel + toll at junctions). If multiple routes have the same least cost, traffic distributes evenly among them.
Question 1 of 5
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 junctions 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.
0,5,2,3
- E.
0,5,2,2
0,5,2,2
Explanation
Checking option (5) (Tolls: A=0, B=5, C=2, D=2):
- SAT =
- SBAT =
- SBCT =
- SDCT =
- SDT = (> 14, so no traffic on SDT). Since SAT, SBAT, SBCT, SDCT all equal 14, traffic distributes equally, ensuring zero traffic on D-T street.
Question 2 of 5
If the government wants to ensure that all motorists travelling from S to T pay the same amount (fuel costs and toll 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 toll charged (in rupees) 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.
2,3,5,1
- E.
1,3,5,1
0,5,3,1
Explanation
With B-C unusable, routes are SAT, SBAT, SDCT, SDT. Fuel costs: SAT=14, SBAT=9, SDCT=10, SDT=13. SAT - SDT = Toll at D must be 1 more than Toll at A. Option (2) gives A=0, D=1. SBAT needs toll B=5 to match 14.
Question 3 of 5
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.
1,5,3,2
- E.
0,4,3,2
0,5,4,1
Explanation
To distribute traffic equally along S-A, S-B, S-D (33.3% each): Option (1) gives tolls (0, 5, 4, 1): Routes cost: SAT = 14, SBAT = 16, SBCT = 14, SDCT = 14, SDT = 14. Traffic on S-A goes via SAT. Traffic on S-B goes via SBCT. Traffic on S-D goes via SDCT and SDT. Each street from S gets equal proportion of traffic.
Question 4 of 5
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
- E.
1,5,4,2
1,5,3,2
Explanation
All 5 routes must have equal total cost. Fuel costs: SAT=14, SBAT=9, SBCT=7, SDCT=10, SDT=13. SAT - SDT = 1 Toll(D) - Toll(A) = 1. SAT - SBCT = 7 Toll(B) + Toll(C) - Toll(A) = 7. Option (4): A=1, B=5, C=3, D=2 matches all conditions.
Question 5 of 5
The government wants to devise a toll policy such that the total cost to the commuters per trip is minimized. The policy should also ensure that not more than 70 per cent of the total traffic passes through junction B. The cost incurred by the commuter travelling from point S to point T under this policy will be:
- A.
Rs. 7
- B.
Rs. 9
- C.
Rs. 10
- D.
Rs. 13
- E.
Rs. 14
Rs. 10
Explanation
If toll policy sets total travel cost = Rs 10, traffic can be directed through SDCT (fuel cost 10) which bypasses B completely, or with appropriate tolls, traffic through B is kept below 70%. Rs 10 is the minimum cost achieving this.
Practise this under exam conditions
Sign in to solve it with a live timer, the on-screen CAT calculator, and streak and accuracy tracking across every question you attempt.
Solve in the workspace