Rake means the coaches or series of coaches used by passengers. The RSA means the Rake is shared by two or more than two trains. For example, the Lucknow Chandigarh Sadhbhavna S/F express, on arrival at Chandigarh, departs as Unchahar express to Allahabad. Similarly, the Unchahar express, on its arrival at Chandigarh departs as Sadhbhavna S/F express to Lucknow. This is done to optimize the usage of racks and reduce the idle time of rakes at particular station to mimimum. There are many other examples also.
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Rake share arrangement or RSA means...
more... the scenario where the incoming rake of one train is used for the outgoing rake of the other-this is to ensure optimizing the use of rakes and minimizing idling time.