Routes and Networks

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Direction: A significant amount of traffic flows from point S to point T in the one-way street network shown below.
Points A, B, C and D are junctions in the network, and the arrows mark the direction of traffic flow.
The fuel cost in rupees for travelling along a street is indicated by the number adjacent to the arrow representing the street.
Motorists travelling from point S to point T would obviously take the route for which the total cost of travelling is the minimum.
If two or more routes have the same least travel cost, then motorists are indifferent between them.
Hence, the traffic gets evenly distributed among all the least cost routes The government can control the flow of traffic only by levying appropriate toll at each junction.
For example, if a motorist takes the route S - A - T (using junction A alone), then the total cost of travel would be Rs 14 (i.e. Rs 9 + Rs 5) plus the toll charged at junction A.

  1. 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 :










  1. View Hint View Answer Discuss in Forum

    As per the given figure , we can see that
    Let the toll charged at junctions A, B, C and D be a, b, c and d respectively.
    Then 1st we will list down all the routes and corresponding cost of travel.
    Since Route BC is under repair hence route S-B-C-T is not in use.
    Rest all four have the same toll charges hence 14 + a = 9 + a + b ⇒ b = 14 - 9 = 5

    Correct Option: E

    As per the given figure , we can see that
    Let the toll charged at junctions A, B, C and D be a, b, c and d respectively.
    Then 1st we will list down all the routes and corresponding cost of travel.
    Since Route BC is under repair hence route S-B-C-T is not in use.
    Rest all four have the same toll charges hence 14 + a = 9 + a + b ⇒ b = 14 - 9 = 5
    Similarly 10 + c + d = 13 + d ⇒ c = 13 - 10 = 3
    Hence Options 4 is ruled out, now if we check option rest 3 options we will find out that option 2 and 3 both are correct. Option (2)/(3) Inconsistent options .


  1. 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 :










  1. View Hint View Answer Discuss in Forum

    Let the toll charged at junctions A, B, C and D be a, b, c and d respectively.
    Then 1st we will list down all the routes and corresponding cost of travel.
    Here in this case all 5 routes have the same toll charge hence 14 + a = 7 + b + c = 13 + d = 9 + a + b = 10 + c + d

    Correct Option: D

    As per the given diagram , we can see that
    Let the toll charged at junctions A, B, C and D be a, b, c and d respectively.
    Then 1st we will list down all the routes and corresponding cost of travel.
    Here in this case all 5 routes have the same toll charge hence 14 + a = 7 + b + c = 13 + d = 9 + a + b = 10 + c + d
    After solving we will get a = 1, b = 5, c = 3 and d = 2


  1. 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 percent 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:










  1. View Hint View Answer Discuss in Forum

    On the basis of above given question , we can say that
    There must be one other route other than those involving B.
    We must take S - D - C - T as the other route.
    S - B - C - T, if toll at B = 3, total cost = 10

    Correct Option: C

    On the basis of above given question , we can say that
    There must be one other route other than those involving B.
    We must take S - D - C - T as the other route.
    S - B - C - T, if toll at B = 3, total cost = 10
    S - D - C - T, if toll at D and C is 0, total cost is 10.
    Hence ,$ 10 is the least cost.

  1. 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:










  1. View Hint View Answer Discuss in Forum

    According to question ,
    If all the five routes have the same cost, then there will be an equal flow in all the five routes, i.e. 20% in each route.
    But then the percentage of traffic in S - A = 20% (Only one route involving S-A)
    S - B = 40% (As there are two routes involving S - B)
    S - D = 40% (As there are two routes involving S - D)
    But here the given condition that traffic in S - A is equal to that in S - B, which in turn is equal to S - D is not satisfied.

    Correct Option: A

    According to question ,
    If all the five routes have the same cost, then there will be an equal flow in all the five routes, i.e. 20% in each route.
    But then the percentage of traffic in S - A = 20% (Only one route involving S - A)
    S - B = 40% (As there are two routes involving S - B)
    S - D = 40% (As there are two routes involving S - D)
    But here the given condition that traffic in S-A is equal to that in S - B, which in turn is equal to S - D is not satisfied.
    Of the routes, that can be used the number of routes involving S - A must be the same as S - B, which in turn is same as that as S - D.
    That is possible only when we block the junction C and that can be done by taking higher toll charge at C to achieve this goal c > 3.
    Hence , required answer will be option A .

  1. 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










  1. View Hint View Answer Discuss in Forum

    Let the toll charged at junctions A, B, C and D be a, b, c and d respectively.
    Then 1st we will list down all the routes and corresponding cost of travel.
    Since the cost of travel including toll on routes S-A-T, S-B-C-T, S-B-A-T and S-D-C-T is the same. And D-T has no traffic due to high toll charge at D.

    Correct Option: E

    From the given diagram ,
    Let the toll charged at junctions A, B, C and D be a, b, c and d respectively.
    Then 1st we will list down all the routes and corresponding cost of travel.
    Since the cost of travel including toll on routes S-A-T, S-B-C-T, S-B-A-T and S-D-C-T is the same. And D-T has no traffic due to high toll charge at D.
    From the last solutions we will get b = 5, 14 + a = 7 + b + c = 12 + c, or a + 2 = c 7 + b + c = 10 + c + d = 12 + c or d = 2, hence the result is B = 5, d = 2 and c-a = 2 that is satisfied by option (E).