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28 May 2015 Last updated at 05:08 BST
Ranjit Power was reported missing on 14 May, a week after he went to India on business.
His daughter Emma Power said: "I'm trying my very, very best to not think the worst."
BBC Midlands Today's Giles Latcham reports.
A missing Wolverhampton hotelier could have been kidnapped in India, his family have said.