# Train problem: No of trains and cross points

Here is a real world problem.
• Train takes 33 hours to reach from Secundarabad (SC) to Patna (PNBE).
• Train from SC leaves @ 10:00 every day
• Train From PNBE leaves @ 12:00 every day
• There is single route for each sides.
• Off-course when one train from one station reaches to other, it will be ready for next departure to back to origin station.
Assuming Train is always at right time (this statement is hypothetical ðŸ˜˜) find followings
1. How many trains needed to operate this route?
2. How many cross point will happen by a train during journey with its co-trains?

## Replies

• Igneta D'Souza
ianoop
Here is a real world problem.
• Train takes 33 hours to reach from Secundarabad (SC) to Patna (PNBE).
• Train from SC leaves @ 10:00 every day
• Train From PNBE leaves @ 12:00 every day
• There is single route for each sides.
• Off-course when one train from one station reaches to other, it will be ready for next departure to back to origin station.
Assuming Train is always at right time (this statement is hypothetical ðŸ˜˜) find followings
1. How many trains needed to operate this route?
2. How many cross point will happen by a train during journey with its co-trains?
1. Five Trains.
what is a cross point?
• Anoop Kumar
what is a cross point?
While journey how many times a train from one side will cross the train coming from other side.
Can you justify why not 4 trains would be enough?

PS: this is real world problem check trains (12791/12792) on IRCTC.co.in or erail.in . I am also don't know exact answer.
• Igneta D'Souza
ianoop
While journey how many times a train from one side will cross the train coming from other side.
Can you justify why not 4 trains would be enough?

PS: this is real world problem check trains (12791/12792) on IRCTC.co.in or erail.in . I am also don't know exact answer.
oops! sorry. It should be four trains.
If a train starts at 10.00, it will reach PNBE the next day at 19.00. The number of 10hrs and 12hrs in this 33hr gap is four. Therefore 4 trains are needed to operate this route.

2)3 cross points will happen with its co-trains.
• Jeffrey Arulraj
igneta
2)3 cross points will happen with its co-trains.
And this part is really puzzling me How is it that has 3 alone

I am of the opinion that there can be 4 cross over as the (n-1)th train will also cross over right

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