Final answer:
The correct authors from the provided options are Salman Rushdie and, by association, Chinua Achebe, although Achebe was Nigerian (option d) and the question seems to have a mistake as R. K. Narayan should be considered.
Step-by-step explanation:
The authors from India who lived in England for a period and returned to India are R. K. Narayan and Salman Rushdie. R.K. Narayan is a well-known Indian writer noted for his works set in the fictional South Indian town of Malgudi. Narayan lived for a while in England before returning to India where he continued his writing career. Salman Rushdie, another prominent author, was born in India, lived in the UK where he established himself as a writer, and although faced with controversy, occasionally returned to India. His novel Midnight's Children articulates postcolonial concerns through a mix of Eastern and Western references, magic, and myth.
Therefore, the correct answer to the student's question would be that option d) Chinua Achebe and Salman Rushdie are the authors who fit the description, although it should be noted that Chinua Achebe was Nigerian, not Indian. Of the two, only Salman Rushdie is associated with India. If the intent is to identify two authors specifically from India, then none of the provided options correctly lists two authors who fulfill the criteria as stated, since R. K. Narayan is not explicitly mentioned in any of the choices.