Train from Nagpur to Raipur

This is an old trick question.

Without loss of generality we can imagine that we are sitting on the train leaving from Nagpur at 7 a.m., before the train that left Raipur at 12.30 a.m. arrives, but after the arrival of 11.30 p.m. departure. That train will arrive at Raipur at noon, after the 11.30 a.m. departure but before the 12.30 p.m. departure.

So during the journey we will encounter the trains that departed from Raipur any half hour between midnight and noon. That is 12 trains.

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No need to calculate the times of the encounters.

A Raipur-bound train is only going to meet Nagpur-bound trains. And we can draw a diagram for that:

The answer is $12$ trains.