So, there's a train traveling from Station A to E, passing through B, C, and D. The train has a seating capacity of 200. Tickets can only be booked from a station to a station ahead, not behind. Also, a ticket from one station to another reserves a seat on every intermediate segment. For example, a ticket from B to E would reserve seats on B-C, C-D, and D-E.
The occupancy factor is the total seats reserved in a segment as a percentage of the seating capacity. So, if 190 seats are reserved on a segment, the occupancy factor is 95%. Also, the total seats reserved for any segment can't exceed 200.
Now, let's look at the given information:
1
Segment C-D had an occupancy factor of 95%. Only segment B-C had a higher occupancy factor. So, B-C must have had 100% occupancy because it's the only one higher than 95%.
2
Exactly 40 tickets were booked from B to C and 30 from B to E.
3
Among the seats reserved on segment D-E, exactly four-sevenths were from stations before C. So, four-sevenths are from A or B, and three-sevenths are from C or D.
4
The number of tickets booked from A to C was equal to that booked from A to E, and it was higher than that from B to E. So, A-C = A-E > B-E (which is 30).
5
No tickets were booked from A to B, from B to D, and from D to E. So, A-B: 0, B-D: 0, D-E: 0.
6
The number of tickets booked for any segment was a multiple of 10.
We need to find the occupancy factor for segment D-E.
Let me try to structure this.
First, let's note the segments:
A-B, B-C, C-D, D-E.
But tickets can be booked from any station to any ahead, so possible tickets are:
A-B, A-C, A-D, A-E,
B-C, B-D, B-E,
C-D, C-E,
D-E.
But from point 5, A-B, B-D, D-E have 0 tickets.
So, tickets booked are:
A-C, A-D, A-E,
B-C, B-E,
C-D, C-E.
Now, let's denote:
Let’s define variables:
Let’s let:
a = number of tickets from A-C
b = number of tickets from A-D
c = number of tickets from A-E
d = number of tickets from B-C (given as 40)
e = number of tickets from B-E (given as 30)
f = number of tickets from C-D
g = number of tickets from C-E
We know from point 4 that a = c and a > e (which is 30). So, a = c > 30.
From point 2, d = 40, e = 30.
From point 3, on segment D-E, four-sevenths of the seats are from stations before C. So, the seats reserved on D-E are from A, B, C, D. But since D-E is the last segment, the tickets that contribute to D-E are those that start from A, B, C, or D and end at E.
But from point 5, D-E has 0 tickets booked, so all the seats on D-E are reserved through tickets from A-E, B-E, C-E.
Wait, no. Wait, D-E is a segment, but tickets booked from D-E would be 0 because you can't book a ticket from D to E if you're already at D. Wait, no, the problem says no tickets were booked from D to E, so D-E has 0 tickets booked. But the seats on D-E are reserved through other tickets. For example, a ticket from C-E would reserve a seat on C-D and D-E.
So, the seats on D-E are reserved by tickets from C-E and B-E (but B-E goes through C-D and D-E). Wait, no, B-E would go through B-C, C-D, D-E. So, each ticket from B-E would reserve a seat on B-C, C-D, D-E.
Similarly, a ticket from C-E would reserve a seat on C-D and D-E.
And tickets from A-E would reserve seats on A-B (but A-B has 0 tickets), A-C, C-D, D-E. Wait, no, A-E would go through A-B (0), A-C, C-D, D-E. But since A-B has 0 tickets, does that mean A-E tickets don't contribute to A-B? Wait, no, because A-E is a direct ticket, but since A-B is not booked, maybe the train goes from A to C directly, so A-E would go through A-C, C-D, D-E.
Wait, I'm getting confused. Let me clarify.
Each ticket from a station to another ahead reserves seats on all intermediate segments. So, a ticket from A-E would reserve seats on A-B, B-C, C-D, D-E. But since A-B has 0 tickets, does that mean that the seat on A-B is not reserved? Or does it mean that the ticket from A-E doesn't exist because A-B is not booked? No, the problem says that tickets can be booked from any station to any ahead, but the seats on the intermediate segments are reserved regardless of whether tickets are booked on those segments. So, even if A-B has 0 tickets, a ticket from A-E would still reserve a seat on A-B, but since no one is booking A-B, maybe that seat isn't actually occupied? Wait, no, the occupancy factor is based on the number of seats reserved, regardless of whether the intermediate segments have tickets or not.
Wait, no, the occupancy factor is the total seats reserved in the segment as a percentage of the seating capacity. So, even if a segment has no tickets booked directly, if other tickets pass through it, those contribute to the occupancy.
So, for example, segment B-C has tickets booked directly (d=40) and also tickets from B-E (e=30) and A-C (a) and A-E (c). Wait, no, A-C would go through A-B (0) and B-C. So, each A-C ticket would reserve a seat on B-C. Similarly, A-E would go through A-B (0), B-C, C-D, D-E. So, each A-E ticket would reserve seats on B-C, C-D, D-E.
Similarly, B-E tickets (e=30) would reserve seats on B-C, C-D, D-E.
C-E tickets (g) would reserve seats on C-D and D-E.
So, the
