CAT 2022 Slot 1 — DILR Question 1
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Given above is the schematic map of the metro lines in a city with rectangles denoting terminal stations (e.g. A), diamonds denoting junction stations (e.g. R) and small filled-up circles denoting other stations. Each train runs either in east-west or north-south direction, but not both. All trains stop for 2 minutes at each of the junction stations on the way and for 1 minute at each of the other stations. It takes 2 minutes to reach the next station for trains going in east-west direction and 3 minutes to reach the next station for trains going in north-south direction. From each terminal station, the first train starts at 6 am; the last trains leave the terminal stations at midnight. Otherwise, during the service hours, there are metro service every 15 minutes in the north-south lines and every 10 minutes in the east west lines. A train must rest for at least 15 minutes after completing a trip at the terminal station, before it can undertake the next trip in the reverse direction. (All questions are related to this metro service only. Assume that if someone reaches a station exactly at the time a train is supposed to leave, (s)he can catch that train.)
If Hari is ready to board a train at 8:05 am from station M, then when is the earliest that he can reach station N?
Answer & solution
- A
9:06 am
- B
9:01 am
- C
9:13 am
9:11 am
A train leaves M every 10 minutes starting at 6 am.
If Hari reaches M at 8:05, he can catch the train that leaves at 8:10 am.
Time taken by Hari to reach N:
There are total 20 stations from M till N, hence total travelling time = 20 × 2 = 40 minutes.
There are 2 junctions, hence stoppage time = 2 × 2 = 4 mins
There are 17 other stations, hence stoppage time = 17 × 1 = 17 mins
∴ Total time taken = 40 + 4 + 17 = 61 mins.
∴ Hari reaches N at 8:10 am + 61 minutes = 9:11 am.
Hence, option (d).