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  • Four cars need to travel from Akala (A) to Bakala (B). Two routes are available, one via Mamur (M) and the other via Nanur (N). The roads from A to M, and from N to 8, are both short and narrow. In

Four cars need to travel from Akala (A) to Bakala (B). Two routes are available, one via Mamur (M) and the other via Nanur (N). The roads from A to M, and from N to 8, are both short and narrow. In each case, one car takes 6 minutes to cover the distance, and each additional car increases the travel time per car by 3 minutes because of congestion. (For example, if only two cars drive from A to M, each car takes 9 minutes.) On the road from A to N, one car takes 20 minutes, and each additional car increases the travel time per car by 1 minute. On the road from M to B, one car takes 20 minutes, and each additional car increases the travel time per car by 0.9 minute.
 

The police department orders each car to take a particular route in such a manner that it is not possible for any car to reduce its travel time by not following the order, while the other cars are following the order. 

Question : How many cars would be asked to take the route A-N-B, that is Akala-Nanur-Bakala route, by the police department?

Option: 1

2


Option: 2

-


Option: 3

-


Option: 4

-


Answers (1)

best_answer

Below can be inferred:

  • The travel time through each route is nearly the same.
  • If 3 cars were directed to go through any of the routes, one of the 3 cars could break the police order and reduce its travel time.
  • Therefore, 2 cars should go through each route.

Here is a table showing the travel times for each route:

    Route

    Travel time for 1 car

    Travel time for 2 cars

    A-M-B

    6 minutes + 3 minutes/car * (number of cars -     1)

    12 minutes + 6 minutes/car * (number of cars -     1)

    A-N-B

    20 minutes + 1 minute/car * (number of cars -     1)

    40 minutes + 2 minutes/car * (number of cars -     1)

As you can see, the travel time for each route is nearly the same. Therefore, it is optimal to send 2 cars through each route.

In addition, if 3 cars were directed to go through any of the routes, one of the 3 cars could break the police order and reduce its travel time. For example, if 3 cars were directed to go through route A-M-B, one of the cars could take route A-N-B instead and save 3 minutes.

Therefore, the police department would ask 2 cars to take the route A-N-B.

 

Posted by

shivangi.shekhar

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