Poorabiya Express: कोसी की शान से दिल्ली महान तक - Md Rashid Alam

I am not going into any manual calculation part. However assuming, you had a connecting (telescopic) ticket, your starting train was running late => You missed the connecting train + Your connecting train was running late => You wanted to cancel the 2nd part of the ticket.
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Now as you said, SM agreed for 50% refund. Now if this had been a telescopic ticket, he should have granted you refund = Total fare - Fare of distance traveled. (Since connecting train was running late you could still cancel the 2nd ticket else...
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you would have to file a TDR).
Thus, in all possibility I cannot take this to be a telescopic ticket. Instead this should have been separate tickets.
Now if at all such situation has to arise in case of telescopic (connecting) tickets, if the delay of the starting train or the connecting train is announced well in advance (Like it was for some trains during the night block in the TATA region), system shall not grant you full refund.