Doubt on Indian Airports Immigration counter

[Braandan]

Question:
A person , Indian passport holder, is having a valid long term visa to a foriegn country in his passport when he entered India. During his stay in India his passport expired and he got a new passport issued to him (Indian passport). When he travels back to the said foriegn country, will he be allowed to depart by showing his old and new passports. The visa is stamped in the old passport and not in the new one.

The question is not about the foreign country immigration, please note. There is no worry about the foreign country once he lands up there. This is only about how he would be treated at the Indian airport immigration counter.