The Smart Scholars' Method

It is obvious that the four persons, in descending order of age, are: Brajesh, Madhuri, Mithun and Chitra. No two of them can be of the same age.

From (3), the doctor cannot be a man and hence Chitra or Madhuri is the doctor.

CASE I: Doctor is a woman and banker is also a woman. Then, from (1), the banker is Madhuri (because she has to be older) and the doctor is Chitra.
 

CASE II: Doctor is a woman and banker is a man. Then, from (4), the banker is Brajesh (because he has to be older) and the doctor is Chitra.
 

In either case, the doctor is Chitra. 

Sanity check:

With Chitra for the doctor, we can see that all the five conditions can be satisfied.
 

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