CAT 2017 Slot 1 — DILR Question 30
Answer the following question based on the information given below.
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 B, 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, 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.
If all the cars follow the police order, what is the difference in travel time (in minutes) between a car which takes the route A-N-B and a car that takes the route A-M-B?
Answer & solution
- A
1
0.1
- C
0.2
- D
0.9
The police department would ask 2 cars to take the A-N-B route and 2 cars to take the A-M-B route, because 2 cars taking each of these routes would minimize the time for each of the 4 cars.
2 cars taking A-M-B route – 9 + 20.9 = 29.9 minutes.
2 cars taking A-N-B route – 21 + 9 = 30 minutes.
Increasing to 3 cars on the A-M-B would increase travel time of each car by 4.8 minutes and increasing to 3 cars on the A-N-B route would increase travel time of each car by 4 minutes.
Minimum travel time would be when 2 cars are assigned to each of the 2 routes by the police department.
The difference in travel time when the cars follow the police order is 30-29.9 or 0.1 minutes.
Hence, option (b).