The word doing the work in this stem is "first". Nobody is asking whether the family should ever be told or whether HIV status is confidential. The question is about sequence, and sequence questions are decided by ranking the interests at stake. Mr. Samay is unconscious, he needs an urgent operation, and his HIV status has just surfaced. Line up the interests: his life, his privacy, his family's wish to know, and his employer's curiosity. Then ask which one, if ignored for even an hour, cannot be repaired.
So option (A) is the answer, on the simple ground that saving the life comes first and everything else is arranged afterwards.
Let's summarize:
Since the operation is what cannot wait, the doctors should operate first and option (A) is correct.