Route based
Q.No: 1
Test Name : CAT Actual Paper 2022 Slot-1
Question Numbers (40 to 44):
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.)
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?
Solution:
Given that Hari is ready to board a train at 8:05 am from station M.
Trains leave after every 10 minutes. So Hari can catch the 8:10 train from M.
There are 17 stations, 2 junctions and 20 intervals, so time taken to travel = 20 × 2 + 17 × 1 + 2 × 2 = 61 minutes
Hence, time at which Hari reaches station N = 8:10 + 1:01 = 9:11 am.
Given that Hari is ready to board a train at 8:05 am from station M.
Trains leave after every 10 minutes. So Hari can catch the 8:10 train from M.
There are 17 stations, 2 junctions and 20 intervals, so time taken to travel = 20 × 2 + 17 × 1 + 2 × 2 = 61 minutes
Hence, time at which Hari reaches station N = 8:10 + 1:01 = 9:11 am.
Q.No: 2
Test Name : CAT Actual Paper 2022 Slot-1
Question Numbers (40 to 44):
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.)
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?
Solution:
There can be two routes that Priya can take.
Case 1: First travel by East-West line and then North-South line.
Trains leave after every 10 minutes on the East- West line.
The 10:20 am train from P reaches and then leaves T at = 10:20 + 00:11 + 00:02 = 10:33 am In the first case Priya will have to wait for 8 minutes at the station before boarding the train.
So let us see if the waiting time is reduced in case 2.
Case 2: First travel by North-South line and then East-West line.
Trains leave after every 15 minutes on the North- South line. The 10:15 am train from B will reach T at = 10:15 + 00:11 = 10:26 am and leave T at 10:28 am. In this case Priya’s train leaves within 3 minutes of her reaching the station. This train reaches R at = 10:28 + 00:15 = 10:43 am.
From R Priya has to catch the East-West train for station S.
The 10:30 am train from M reaches R at = 10:30 + 00:11 = 10:41 am and leaves at 10:43 am.
Priya can catch this train and reach station S at = 10:43 + 00:29 = 11:12 am.
There can be two routes that Priya can take.
Case 1: First travel by East-West line and then North-South line.
Trains leave after every 10 minutes on the East- West line.
The 10:20 am train from P reaches and then leaves T at = 10:20 + 00:11 + 00:02 = 10:33 am In the first case Priya will have to wait for 8 minutes at the station before boarding the train.
So let us see if the waiting time is reduced in case 2.
Case 2: First travel by North-South line and then East-West line.
Trains leave after every 15 minutes on the North- South line. The 10:15 am train from B will reach T at = 10:15 + 00:11 = 10:26 am and leave T at 10:28 am. In this case Priya’s train leaves within 3 minutes of her reaching the station. This train reaches R at = 10:28 + 00:15 = 10:43 am.
From R Priya has to catch the East-West train for station S.
The 10:30 am train from M reaches R at = 10:30 + 00:11 = 10:41 am and leaves at 10:43 am.
Priya can catch this train and reach station S at = 10:43 + 00:29 = 11:12 am.
Q.No: 3
Test Name : CAT Actual Paper 2022 Slot-1
Question Numbers (40 to 44):
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.)
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.)
Haripriya is expected to reach station S late. What is the latest time by which she must be ready to board at station S if she must reach station B before 1 am via station R?
Solution:
The last (midnight) train from A reaches R at 12:11 am and leaves at 12:13 am. It will reach B at = 12:13 + 00:17 + 00:11 = 12:41 am.
From S to R the travel time is 29 minutes. To catch the 12:13 am train Haripriya will have to start from S at = 12:13 – 00:29 = 11:44 pm or before that.
Trains start from N after every 10 minutes and the time taken to reach S is 17 minutes.
There is a stoppage of 2 minutes at S.
The 11:30 pm train from N reaches S at 11:47 pm, which does not serve the purpose.
The 11:20 pm train from N reaches S at 11:37 pm and leaves at 11:39 pm.
This train will reach R by 11:39 + 00:29 = 12:08 am.
Then she can catch the last train from A going to B at 12:13 am.
Haripriya can catch the train at S if she reaches the station latest by 11:39 pm.
The last (midnight) train from A reaches R at 12:11 am and leaves at 12:13 am. It will reach B at = 12:13 + 00:17 + 00:11 = 12:41 am.
From S to R the travel time is 29 minutes. To catch the 12:13 am train Haripriya will have to start from S at = 12:13 – 00:29 = 11:44 pm or before that.
Trains start from N after every 10 minutes and the time taken to reach S is 17 minutes.
There is a stoppage of 2 minutes at S.
The 11:30 pm train from N reaches S at 11:47 pm, which does not serve the purpose.
The 11:20 pm train from N reaches S at 11:37 pm and leaves at 11:39 pm.
This train will reach R by 11:39 + 00:29 = 12:08 am.
Then she can catch the last train from A going to B at 12:13 am.
Haripriya can catch the train at S if she reaches the station latest by 11:39 pm.
Q.No: 4
Test Name : CAT Actual Paper 2022 Slot-1
Question Numbers (40 to 44):
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.)
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.)
What is the minimum number of trains that are required to provide the service on the AB line (considering both north and south directions)?
Solution:
Total time for a train to travel from A to B and to start back = 11 + 2 + 15 + 2 + 11 + 15 = 56 minutes.
Trains leave after every 15 minutes.
The minimum number of trains that are required to provide the service on the AB line (in the North-South direction) = [56/15] = [3.733] = 4 trains
Hence, for both directions = 4 + 4 = 8 trains.
Total time for a train to travel from A to B and to start back = 11 + 2 + 15 + 2 + 11 + 15 = 56 minutes.
Trains leave after every 15 minutes.
The minimum number of trains that are required to provide the service on the AB line (in the North-South direction) = [56/15] = [3.733] = 4 trains
Hence, for both directions = 4 + 4 = 8 trains.
Q.No: 5
Test Name : CAT Actual Paper 2022 Slot-1
Question Numbers (40 to 44):
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.)
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.)
What is the minimum number of trains that are required to provide the service in this city?
Solution:
The minimum number of trains that are required to provide the service in this city
= Trains in AB and CD lines + Trains in MN and PQ lines.
Time taken for a train to travel from M to N and start back
= 11 + 2 + 29 + 2 + 17 + 15 = 76 minutes.
Trains leave after every 10 minutes on this line.
The minimum number of trains required on the MN line in the East-West direction
= [76/10] = [7.6] = 8 trains
Minimum number of trains required in both directions on the MN line = 16 trains Hence, total number of trains required
= (AB + CD) + (MN + PQ) = (8 + 8) + ( 16 + 16) = 48.
The minimum number of trains that are required to provide the service in this city
= Trains in AB and CD lines + Trains in MN and PQ lines.
Time taken for a train to travel from M to N and start back
= 11 + 2 + 29 + 2 + 17 + 15 = 76 minutes.
Trains leave after every 10 minutes on this line.
The minimum number of trains required on the MN line in the East-West direction
= [76/10] = [7.6] = 8 trains
Minimum number of trains required in both directions on the MN line = 16 trains Hence, total number of trains required
= (AB + CD) + (MN + PQ) = (8 + 8) + ( 16 + 16) = 48.
Q.No: 6
Test Name : CAT Actual Paper 2023 Slot 3
Question Numbers (35 to 39): A, B, C, D, E and F are
the six police stations in an area, which are connected
by streets as shown below. Four teams – Team 1, Team
2, Team 3 and Team 4 –
patrol these streets continuously between 09:00 hrs. and 12:00 hrs. each day.
The teams need 30 minutes to cross a street connecting one police station to another. All four teams start from Station A at 09:00 hrs. and must return to Station A by 12:00 hrs. They can also pass via Station A at any point on their journeys.
The following facts are known.
1. None of the streets has more than one team traveling along it in any direction at any point in time.
2. Teams 2 and 3 are the only ones in stations E and D respectively at 10:00 hrs.
3. Teams 1 and 3 are the only ones in station E at 10:30 hrs.
4. Teams 1 and 4 are the only ones in stations B and E respectively at 11:30 hrs.
5. Team 1 and Team 4 are the only teams that patrol the street connecting stations A and E.
6. Team 4 never passes through Stations B, D or F.
patrol these streets continuously between 09:00 hrs. and 12:00 hrs. each day.
The teams need 30 minutes to cross a street connecting one police station to another. All four teams start from Station A at 09:00 hrs. and must return to Station A by 12:00 hrs. They can also pass via Station A at any point on their journeys.
The following facts are known.
1. None of the streets has more than one team traveling along it in any direction at any point in time.
2. Teams 2 and 3 are the only ones in stations E and D respectively at 10:00 hrs.
3. Teams 1 and 3 are the only ones in station E at 10:30 hrs.
4. Teams 1 and 4 are the only ones in stations B and E respectively at 11:30 hrs.
5. Team 1 and Team 4 are the only teams that patrol the street connecting stations A and E.
6. Team 4 never passes through Stations B, D or F.
How many times do the teams pass through Station B in a day?
Solution:
The number of times the teams pass through station B = 2.
The number of times the teams pass through station B = 2.
Q.No: 7
Test Name : CAT Actual Paper 2023 Slot 3
Question Numbers (35 to 39): A, B, C, D, E and F are
the six police stations in an area, which are connected
by streets as shown below. Four teams – Team 1, Team
2, Team 3 and Team 4 –
patrol these streets continuously between 09:00 hrs. and 12:00 hrs. each day.
The teams need 30 minutes to cross a street connecting one police station to another. All four teams start from Station A at 09:00 hrs. and must return to Station A by 12:00 hrs. They can also pass via Station A at any point on their journeys.
The following facts are known.
1. None of the streets has more than one team traveling along it in any direction at any point in time.
2. Teams 2 and 3 are the only ones in stations E and D respectively at 10:00 hrs.
3. Teams 1 and 3 are the only ones in station E at 10:30 hrs.
4. Teams 1 and 4 are the only ones in stations B and E respectively at 11:30 hrs.
5. Team 1 and Team 4 are the only teams that patrol the street connecting stations A and E.
6. Team 4 never passes through Stations B, D or F.
patrol these streets continuously between 09:00 hrs. and 12:00 hrs. each day.
The teams need 30 minutes to cross a street connecting one police station to another. All four teams start from Station A at 09:00 hrs. and must return to Station A by 12:00 hrs. They can also pass via Station A at any point on their journeys.
The following facts are known.
1. None of the streets has more than one team traveling along it in any direction at any point in time.
2. Teams 2 and 3 are the only ones in stations E and D respectively at 10:00 hrs.
3. Teams 1 and 3 are the only ones in station E at 10:30 hrs.
4. Teams 1 and 4 are the only ones in stations B and E respectively at 11:30 hrs.
5. Team 1 and Team 4 are the only teams that patrol the street connecting stations A and E.
6. Team 4 never passes through Stations B, D or F.
How many times does Team 4 pass through Station E in a day?
Solution:
Team 4 passes through station E twice.
Team 4 passes through station E twice.
Q.No: 8
Test Name : CAT Actual Paper 2023 Slot 3
Question Numbers (35 to 39): A, B, C, D, E and F are
the six police stations in an area, which are connected
by streets as shown below. Four teams – Team 1, Team
2, Team 3 and Team 4 –
patrol these streets continuously between 09:00 hrs. and 12:00 hrs. each day.
The teams need 30 minutes to cross a street connecting one police station to another. All four teams start from Station A at 09:00 hrs. and must return to Station A by 12:00 hrs. They can also pass via Station A at any point on their journeys.
The following facts are known.
1. None of the streets has more than one team traveling along it in any direction at any point in time.
2. Teams 2 and 3 are the only ones in stations E and D respectively at 10:00 hrs.
3. Teams 1 and 3 are the only ones in station E at 10:30 hrs.
4. Teams 1 and 4 are the only ones in stations B and E respectively at 11:30 hrs.
5. Team 1 and Team 4 are the only teams that patrol the street connecting stations A and E.
6. Team 4 never passes through Stations B, D or F.
patrol these streets continuously between 09:00 hrs. and 12:00 hrs. each day.
The teams need 30 minutes to cross a street connecting one police station to another. All four teams start from Station A at 09:00 hrs. and must return to Station A by 12:00 hrs. They can also pass via Station A at any point on their journeys.
The following facts are known.
1. None of the streets has more than one team traveling along it in any direction at any point in time.
2. Teams 2 and 3 are the only ones in stations E and D respectively at 10:00 hrs.
3. Teams 1 and 3 are the only ones in station E at 10:30 hrs.
4. Teams 1 and 4 are the only ones in stations B and E respectively at 11:30 hrs.
5. Team 1 and Team 4 are the only teams that patrol the street connecting stations A and E.
6. Team 4 never passes through Stations B, D or F.
How many teams pass through Station C in a day?
Solution:
The number of teams that pass through station C = 2.
The number of teams that pass through station C = 2.
Q.No: 9
Test Name : CAT Actual Paper 2023 Slot 3
Question Numbers (35 to 39): A, B, C, D, E and F are
the six police stations in an area, which are connected
by streets as shown below. Four teams – Team 1, Team
2, Team 3 and Team 4 –
patrol these streets continuously between 09:00 hrs. and 12:00 hrs. each day.
The teams need 30 minutes to cross a street connecting one police station to another. All four teams start from Station A at 09:00 hrs. and must return to Station A by 12:00 hrs. They can also pass via Station A at any point on their journeys.
The following facts are known.
1. None of the streets has more than one team traveling along it in any direction at any point in time.
2. Teams 2 and 3 are the only ones in stations E and D respectively at 10:00 hrs.
3. Teams 1 and 3 are the only ones in station E at 10:30 hrs.
4. Teams 1 and 4 are the only ones in stations B and E respectively at 11:30 hrs.
5. Team 1 and Team 4 are the only teams that patrol the street connecting stations A and E.
6. Team 4 never passes through Stations B, D or F.
patrol these streets continuously between 09:00 hrs. and 12:00 hrs. each day.
The teams need 30 minutes to cross a street connecting one police station to another. All four teams start from Station A at 09:00 hrs. and must return to Station A by 12:00 hrs. They can also pass via Station A at any point on their journeys.
The following facts are known.
1. None of the streets has more than one team traveling along it in any direction at any point in time.
2. Teams 2 and 3 are the only ones in stations E and D respectively at 10:00 hrs.
3. Teams 1 and 3 are the only ones in station E at 10:30 hrs.
4. Teams 1 and 4 are the only ones in stations B and E respectively at 11:30 hrs.
5. Team 1 and Team 4 are the only teams that patrol the street connecting stations A and E.
6. Team 4 never passes through Stations B, D or F.
Which one among the following stations is visited the largest number of times?
Solution:
From the table we can see that station D was visited twice, stations C and F were visited thrice and station E was visited either 5 or 6 times. Hence, station E was visited the maximum number of times.
From the table we can see that station D was visited twice, stations C and F were visited thrice and station E was visited either 5 or 6 times. Hence, station E was visited the maximum number of times.
Q.No: 10
Test Name : CAT Actual Paper 2023 Slot 3
Question Numbers (35 to 39): A, B, C, D, E and F are
the six police stations in an area, which are connected
by streets as shown below. Four teams – Team 1, Team
2, Team 3 and Team 4 –
patrol these streets continuously between 09:00 hrs. and 12:00 hrs. each day.
The teams need 30 minutes to cross a street connecting one police station to another. All four teams start from Station A at 09:00 hrs. and must return to Station A by 12:00 hrs. They can also pass via Station A at any point on their journeys.
The following facts are known.
1. None of the streets has more than one team traveling along it in any direction at any point in time.
2. Teams 2 and 3 are the only ones in stations E and D respectively at 10:00 hrs.
3. Teams 1 and 3 are the only ones in station E at 10:30 hrs.
4. Teams 1 and 4 are the only ones in stations B and E respectively at 11:30 hrs.
5. Team 1 and Team 4 are the only teams that patrol the street connecting stations A and E.
6. Team 4 never passes through Stations B, D or F.
patrol these streets continuously between 09:00 hrs. and 12:00 hrs. each day.
The teams need 30 minutes to cross a street connecting one police station to another. All four teams start from Station A at 09:00 hrs. and must return to Station A by 12:00 hrs. They can also pass via Station A at any point on their journeys.
The following facts are known.
1. None of the streets has more than one team traveling along it in any direction at any point in time.
2. Teams 2 and 3 are the only ones in stations E and D respectively at 10:00 hrs.
3. Teams 1 and 3 are the only ones in station E at 10:30 hrs.
4. Teams 1 and 4 are the only ones in stations B and E respectively at 11:30 hrs.
5. Team 1 and Team 4 are the only teams that patrol the street connecting stations A and E.
6. Team 4 never passes through Stations B, D or F.
Which team patrols the street connecting Stations D and E at 10:15 hrs?
Solution:
The team that is on route D-E at 10:15 is Team 3.
The team that is on route D-E at 10:15 is Team 3.
Solution:
Given that Hari is ready to board a train at 8:05 am from station M.
Trains leave after every 10 minutes. So Hari can catch the 8:10 train from M.
There are 17 stations, 2 junctions and 20 intervals, so time taken to travel = 20 × 2 + 17 × 1 + 2 × 2 = 61 minutes
Hence, time at which Hari reaches station N = 8:10 + 1:01 = 9:11 am.
Given that Hari is ready to board a train at 8:05 am from station M.
Trains leave after every 10 minutes. So Hari can catch the 8:10 train from M.
There are 17 stations, 2 junctions and 20 intervals, so time taken to travel = 20 × 2 + 17 × 1 + 2 × 2 = 61 minutes
Hence, time at which Hari reaches station N = 8:10 + 1:01 = 9:11 am.
Solution:
There can be two routes that Priya can take.
Case 1: First travel by East-West line and then North-South line.
Trains leave after every 10 minutes on the East- West line.
The 10:20 am train from P reaches and then leaves T at = 10:20 + 00:11 + 00:02 = 10:33 am In the first case Priya will have to wait for 8 minutes at the station before boarding the train.
So let us see if the waiting time is reduced in case 2.
Case 2: First travel by North-South line and then East-West line.
Trains leave after every 15 minutes on the North- South line. The 10:15 am train from B will reach T at = 10:15 + 00:11 = 10:26 am and leave T at 10:28 am. In this case Priya’s train leaves within 3 minutes of her reaching the station. This train reaches R at = 10:28 + 00:15 = 10:43 am.
From R Priya has to catch the East-West train for station S.
The 10:30 am train from M reaches R at = 10:30 + 00:11 = 10:41 am and leaves at 10:43 am.
Priya can catch this train and reach station S at = 10:43 + 00:29 = 11:12 am.
There can be two routes that Priya can take.
Case 1: First travel by East-West line and then North-South line.
Trains leave after every 10 minutes on the East- West line.
The 10:20 am train from P reaches and then leaves T at = 10:20 + 00:11 + 00:02 = 10:33 am In the first case Priya will have to wait for 8 minutes at the station before boarding the train.
So let us see if the waiting time is reduced in case 2.
Case 2: First travel by North-South line and then East-West line.
Trains leave after every 15 minutes on the North- South line. The 10:15 am train from B will reach T at = 10:15 + 00:11 = 10:26 am and leave T at 10:28 am. In this case Priya’s train leaves within 3 minutes of her reaching the station. This train reaches R at = 10:28 + 00:15 = 10:43 am.
From R Priya has to catch the East-West train for station S.
The 10:30 am train from M reaches R at = 10:30 + 00:11 = 10:41 am and leaves at 10:43 am.
Priya can catch this train and reach station S at = 10:43 + 00:29 = 11:12 am.
Solution:
The last (midnight) train from A reaches R at 12:11 am and leaves at 12:13 am. It will reach B at = 12:13 + 00:17 + 00:11 = 12:41 am.
From S to R the travel time is 29 minutes. To catch the 12:13 am train Haripriya will have to start from S at = 12:13 – 00:29 = 11:44 pm or before that.
Trains start from N after every 10 minutes and the time taken to reach S is 17 minutes.
There is a stoppage of 2 minutes at S.
The 11:30 pm train from N reaches S at 11:47 pm, which does not serve the purpose.
The 11:20 pm train from N reaches S at 11:37 pm and leaves at 11:39 pm.
This train will reach R by 11:39 + 00:29 = 12:08 am.
Then she can catch the last train from A going to B at 12:13 am.
Haripriya can catch the train at S if she reaches the station latest by 11:39 pm.
The last (midnight) train from A reaches R at 12:11 am and leaves at 12:13 am. It will reach B at = 12:13 + 00:17 + 00:11 = 12:41 am.
From S to R the travel time is 29 minutes. To catch the 12:13 am train Haripriya will have to start from S at = 12:13 – 00:29 = 11:44 pm or before that.
Trains start from N after every 10 minutes and the time taken to reach S is 17 minutes.
There is a stoppage of 2 minutes at S.
The 11:30 pm train from N reaches S at 11:47 pm, which does not serve the purpose.
The 11:20 pm train from N reaches S at 11:37 pm and leaves at 11:39 pm.
This train will reach R by 11:39 + 00:29 = 12:08 am.
Then she can catch the last train from A going to B at 12:13 am.
Haripriya can catch the train at S if she reaches the station latest by 11:39 pm.
Solution:
Total time for a train to travel from A to B and to start back = 11 + 2 + 15 + 2 + 11 + 15 = 56 minutes.
Trains leave after every 15 minutes.
The minimum number of trains that are required to provide the service on the AB line (in the North-South direction) = [56/15] = [3.733] = 4 trains
Hence, for both directions = 4 + 4 = 8 trains.
Total time for a train to travel from A to B and to start back = 11 + 2 + 15 + 2 + 11 + 15 = 56 minutes.
Trains leave after every 15 minutes.
The minimum number of trains that are required to provide the service on the AB line (in the North-South direction) = [56/15] = [3.733] = 4 trains
Hence, for both directions = 4 + 4 = 8 trains.
Solution:
The minimum number of trains that are required to provide the service in this city
= Trains in AB and CD lines + Trains in MN and PQ lines.
Time taken for a train to travel from M to N and start back
= 11 + 2 + 29 + 2 + 17 + 15 = 76 minutes.
Trains leave after every 10 minutes on this line.
The minimum number of trains required on the MN line in the East-West direction
= [76/10] = [7.6] = 8 trains
Minimum number of trains required in both directions on the MN line = 16 trains Hence, total number of trains required
= (AB + CD) + (MN + PQ) = (8 + 8) + ( 16 + 16) = 48.
The minimum number of trains that are required to provide the service in this city
= Trains in AB and CD lines + Trains in MN and PQ lines.
Time taken for a train to travel from M to N and start back
= 11 + 2 + 29 + 2 + 17 + 15 = 76 minutes.
Trains leave after every 10 minutes on this line.
The minimum number of trains required on the MN line in the East-West direction
= [76/10] = [7.6] = 8 trains
Minimum number of trains required in both directions on the MN line = 16 trains Hence, total number of trains required
= (AB + CD) + (MN + PQ) = (8 + 8) + ( 16 + 16) = 48.
Solution:
The number of times the teams pass through station B = 2.
The number of times the teams pass through station B = 2.
Solution:
Team 4 passes through station E twice.
Team 4 passes through station E twice.
Solution:
The number of teams that pass through station C = 2.
The number of teams that pass through station C = 2.
Solution:
From the table we can see that station D was visited twice, stations C and F were visited thrice and station E was visited either 5 or 6 times. Hence, station E was visited the maximum number of times.
From the table we can see that station D was visited twice, stations C and F were visited thrice and station E was visited either 5 or 6 times. Hence, station E was visited the maximum number of times.
Solution:
The team that is on route D-E at 10:15 is Team 3.
The team that is on route D-E at 10:15 is Team 3.
