Routes and Networks


Direction: A city has hexagonal ring road as shown in the figure below. Mr. Ricky stays at X near city and his office is located at Y. The arrow in the figure shows flow of traffic at office hours. The numerical value near each path shows the cost of travel along that road/stretch of the road. There is a fix toll tax at each of toll booths T1, T2...............… T8. The total cost of travel includes cost incurred along the path and at the toll booth.

  1. If a new path is constructed from T7 to Y then find the total number of paths from X to Y?









  1. View Hint View Answer Discuss in Forum

    As per the given above diagram , we can see that
    Total number of paths from X to Y is 7.

    Correct Option: A

    As per the given above diagram , we can see that
    Total number of paths from X to Y is 7.


  1. Which one of the following could be the value of toll taxes at T1, T2, T3…............... T8 such that total cost of travel is same irrespective of route?









  1. View Hint View Answer Discuss in Forum

    From the solution of previous question ,
    we have following results:
    T3 = T7 = 0,
    T1 = 20 + T2 + T4, T5 = 30 + T6 + T8.
    From the given options option B satisfies the condition.

    Correct Option: B

    From the solution of previous question ,
    we have following results:
    T3 = T7 = 0,
    T1 = 20 + T2 + T4, T5 = 30 + T6 + T8.
    From the given options option B satisfies the condition.
    Hence , required answer will be 50, 20, 0, 10, 60, 20, 0, 10 .



  1. What is the difference between maximum amount and minimum amount that Mr. Ricky can spend on a day if he wants to travel from his home (X) to office (Y) if toll tax at each toll booth is Rs 50?









  1. View Hint View Answer Discuss in Forum

    On the basis of above given diagram , we can see that
    Maximum expenditure is in path 3 and that is 260 + 50 x 6 = 260 + 300 = 560
    Minimum expenditure is in path 5 and that is 230 + 50 x 3 = 230 + 150 = 380
    ∴ Required difference = Maximum expenditure is in path 3 - Minimum expenditure is in path 5 = 560 – 380 = 180

    Correct Option: A

    On the basis of above given diagram , we can see that
    Maximum expenditure is in path 3 and that is 260 + 50 x 6 = 260 + 300 = 560
    Minimum expenditure is in path 5 and that is 230 + 50 x 3 = 230 + 150 = 380
    ∴ Required difference = Maximum expenditure is in path 3 - Minimum expenditure is in path 5 = 560 – 380 = 180
    Hence , Required difference is 180.


  1. If toll tax is devised in such a way that total cost of travel remains same irrespective of the path then what is the minimum cost of travel from X to Y?









  1. View Hint View Answer Discuss in Forum

    From the given condition ,
    cost incurred in path 2 is equal to that in path 3 then T3 = 0
    Similarly ,equating cost of path 3 and path 4 T7 = 0
    Equating cost of path 4 and path 5 we will get
    260 + T6 + T8= 230 + T5
    T5 = T6 + T8 + 30
    Equating cost of path 1 and path 2 we will get ,
    240 +T1 = 260 + T2+ T4
    or T1 = T2 + T4 + 20

    Correct Option: B

    From the given condition ,
    cost incurred in path 2 is equal to that in path 3 then T3 = 0
    Similarly ,equating cost of path 3 and path 4 T7 = 0
    Equating cost of path 4 and path 5 we will get
    260 + T6 + T8 = 230 + T5
    T5 = T6 + T8 + 30
    Equating cost of path 1 and path 2 we will get ,
    240 +T1 = 260 + T2+ T4
    or T1 = T2 + T4 + 20
    For minimum total cost T1 = 20 and T5 = 30 then cost incurred is Rs 260.
    Therefore , the minimum cost of travel from X to Y is Rs 260 .



  1. If toll tax at all of the toll booths is same and is devised such that the ratio of maximum cost to minimum cost of travel from X to Y is 28 : 19 then which one of the following is the cost of travel from X to Y through toll Both T3?









  1. View Hint View Answer Discuss in Forum

    If toll tax at all of the toll booths is same and let it be k then expense in each path is as follows:
    Path 1: 240 + 3k
    Path 2: 260 + 5k
    Path 3: 260 + 6k
    Path 4: 260 + 5k
    Path 5: 230 + 3k
    So from the given condition On solving we will get k = 50
    Tool booth 3 will come in Path 3 and Path 4.

    Correct Option: C

    If toll tax at all of the toll booths is same and let it be k then expense in each path is as follows:
    Path 1: 240 + 3k
    Path 2: 260 + 5k
    Path 3: 260 + 6k
    Path 4: 260 + 5k
    Path 5: 230 + 3k
    So from the given condition On solving we will get k = 50
    Tool booth 3 will come in Path 3 and Path 4.
    So cost incurred is:
    Path 3: 260 + 6k = 260 + 300 = 560
    Path 4: 260 + 5k = 260 + 250 = 510
    Therefore , 560 or 510 is the cost of travel from X to Y through toll Both T3 .