CAT 2022 Slot 1 — DILR Question 2
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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 Priya is ready to board a train at 10:25 am from station T, then when is the earliest that she can reach station S?
Answer & solution
11:12 am
- B
11:07 am
- C
11:28 am
- D
11:22 am
Priya can go from T to S via R or V.
Case 1: T – R – S
The first train to depart T will be at (6 am + 9 + 2 + 2 =) 6:13 am.
∴ Now a train will depart T every 15 minutes, hence the train which Priya can catch for T → R is at 10:28.
Time taken to reach R = 12 + 3 = 15 mins.
∴ Priya reaches R at 10:43 am.
The first train to depart R will be at (6 am + 8 + 3 + 2 =) 6:13 am.
∴ Now a train will depart R every 10 minutes, hence the train which Priya can catch for R → S is at 10:43 itself.
Time taken to reach S = 20 + 9 = 29 mins.
∴ Priya reaches S at 11:12 am.
Case 2: T – S – R
The first train to depart T will be at (6 am + 8 + 3 + 2 =) 6:13 am.
∴ Now a train will depart T every 10 minutes, hence the train which Priya can catch for T → V is at 10:33 itself.
Now time taken from T → V is 29 mins and time taken from V → S is 15 mins.
Even if Priya does not have to wait at V she can S latest by 10:33 am + 29 + 15 = 11:17 am.
∴ Priya can reach S latest by 11:12 am.
Hence, option (a).