What is the minimum number of trains that are required to provide the service on the AB line (considering both north and south directions)?
Explanation:
A train leaves A for B and B to A every 15 minutes starting from 6 am.
Total time taken by a north-south train: There are total 10 stations from M till N, hence total travelling time = 10 * 3 = 30 minutes. There are 2 junctions, hence stoppage time = 2 * 2 = 4 mins There are 7 other stations, hence stoppage time = 7 * 1 = 7 mins ∴ Total time taken = 30 + 4 + 7 = 41 mins.
The train which starts from A to B at 6 am reaches B at 6:41 am. It needs to rest for 15 minutes before it can start the journey back to A i.e., it can start it’s journey at 6:56 or after that.
As per schedule north-south trains leave every 15 minutes starting from 6 am. Hence, the train that starts from A to B at 6 am, can start its backward journey at 7 am.
∴ There have to be trains starting at 6 am, 6:15 am, 6:30 am and 6:45 am before trains coming from A can start their journey back.
Hence, we need at least 4 trains from B to A and similarly from A to B.
∴ We need at least 8 trains on the route AB.
Hence, 8.
Help us build a Free and Comprehensive Preparation portal for various competitive exams by providing us your valuable feedback about Apti4All and how it can be improved.