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The prices for regional trains between Aachen and Cologne are set by the transport association VRS (fare level 7).
A single trip costs 17€ per person. A four-trip ticket is available for 61.20€, a day ticket for unlimited travel 28.50€ for one person, 41€ for five persons.
All these tickets are available last-minute at the train station.
Other alternatives would be:
So in conclusion: For two persons returning on the same day a VRS fare level 7 day group ticket for 41€ is the cheapest option. The ticket is also valid for all buses and other transport in Aachen and Cologne on that day.
As this ticket is valid for five persons you might be able to find three other persons for sharing one leg of the ticket at the station.