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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 : 

A new one-way road is built from M to N. Each car now has three possible routes to travel from A to B: A-M-B, A-N-B and A-M-N-B On the road from M to N, one car takes 7 minutes and each additional car increases the travel time per car by 1 minute. Assume that any car taking the A-M-N-B route travels the A-M portion at the same time as other cars taking the A-M-B route, and the N-B portion at the same time as other cars taking the A-N-B route.
 

If all the cars follow the police order, what is the minimum travel time (in minutes) from A to B? (Assume that the police department would never order all the cars to take the same route.) 

Option: 1

26


Option: 2

32


Option: 3

29.9


Option: 4

30


Answers (1)

best_answer
  • If 1 car is ordered to take the A-M-B route, then the travel time for the car is 12 + 20 = 32 minutes.
  • If 2 cars are ordered to take the A-M-N-B route, then the travel time for each car is 12 + 8 + 12 = 32 minutes.
  • If 1 car is ordered to take the A-N-B route, then the travel time for the car is 20 + 12 = 32 minutes.

As you can see, the travel time is the same for each route. Therefore, the minimum travel time is 32 minutes.

Below table shows the travel times for each route:

    Route

    Travel time for 1 car

    A-M-B

    12 + 20 = 32 minutes

    A-M-N-B

    12 + 8 + 12 = 32 minutes

    A-N-B

    20 + 12 = 32 minutes

As you can see, the travel time is the same for each route. Therefore, the minimum travel time is 32 minutes.

 

Posted by

Rishabh

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