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, she can catch that train).
Solution
Understanding the set :-
- This is a routes and networks set, in this type of set you basically get some junction points and multiple routes to reach that point
- In this type of set, after getting a broad idea of the details and clues (if given), will mainly be based on questions of the set.
- In this particular question, we are given metro lines (routes) with their stations (junctions).
- Also, Each train runs either in east-west or north-south direction, but not both
Let’s try to simplify the set using clues given
Clues given to us :-
- 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.
- 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.
First we need to find the time taken from all terminals to all junctions through stations.
M → R = 2 + 2 + 2 + 2(3 stations gap is 4) + 3(every station stop ) = 11 min
P → T = 2 + 2 + 2 + 2 + 3 (same as above) = 11 min
R → S = 2 + 2 + 2+ 2 + 2 + 2 + 2 + 2 + 2 + 2(9 stations so gap is 10) + 9(9 stations ) = 20 min + 9 min = 29 min
T → V = symmetrical as R → S = 20 + 9 = 29 min
S → N = 2 + 2 + 2 + 2 + 2 + 2 + 5 = 12 + 5 = 17 min
V → Q = 12 + 5 = 17 min
A → R = 3 + 3 + 3 + 2 = 11 min
C → S = 3 + 3 + 3 + 2 = 11 min
R → T = 3 + 3 + 3 + 3 + 3 = 15 min
S → V = 3 + 3 + 3 + 3 + 3 = 15 min
T → B = 3 + 3 + 3(for north south direction train takes 3 minutes) + 2 = 11 min
V → D = 3 + 3 + 3 + 2 = 11 min
If Priya is ready to board at 10:25 from station T,
we need to check whether there is a train from P or B around 10:25 am.
As BT path has less number of stations which is 2 so we will take BT path.
- If a train leaves at 10:00 from B it will take 11 minutes to reach T i.e 10:11
=> it would leave at 10:13 so Priya won't be able to catch this train.
- If train leaves at 10:10 from B it will reach T at 10:21
=> it would leave at 10:23 so again she won't be able to catch this train also.
- If train leaves at 10:20 from B it will reach at 10:31 and leave at 10:33
=> which means Priya had to wait for 8 minutes and board this train.
8 min + (T→ R) + (R → S) = 8 min + 15 min + 29 min = 52 min which means she would reach S at 10:33 + 52 min = 11:25 am which is not in option.
- So, we will check the other option ,
As we know for every north-south direction the train can leave after every 15 minutes
Also,If the train leaves from B at 10:15 then it will reach T at 10:26.
It would leave at 10:28 from station T.
So, Priya had waited for 3 minutes.
3 min + (T→R) + (R → S) = 3 + 15 + 29 = 47 minutes
which means she would reach station S at 10:25 + 47 min = 10:25 + 35 min + 12 min = 11:12 min which is option 1