Aisa mat bolo Bhai Bihar mein already rich log hai, for example take Mumbai Patna Suvidha Express, which is a superhit and is not affordable by many. For AC 2 prices go upto 9000 and more. For AC 3 prices come around 6ooo and more. And still people are reserving in that trains even after Flight services between Mumbai & Patna is superhit.
But I'm not sure about Shatabdi as people don't prefer to travel in daytime. According to me possible feasible routes of Shatabdi to Bihar are
1. Patna- Varanasi- Lucknow...
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2. Muzaffarpur- Patliputra- Varanasi- Allahabad