She ____ in Calcutta for a quarter of a century now.
(a)Will live
(b)Lived
(c)Has been living
(d)Had been living

Hint: We use the present perfect continuous tense to indicate an action that began in the past and is continuing in the present. Also, Subject-verb agreement must accord in number. Either both the subject and verb should be singular or both should be plural in number.

Complete answer: As given in the hint, we need to maintain the subject-verb agreement relationship in the above-given sentence.
For example- They have been teaching Hindi for ten years now. Here, we have used the third-person plural verb ‘have’ with the third-person plural pronoun ‘they’, to form appropriate subject-verb agreement.
In the given question- We can conclude that she has been living in Calcutta for a quarter of a century now.
Here, we have used the third-person singular verb ‘has’ with the third person singular pronoun ‘she’. Also, we have used the present perfect continuous tense to indicate an action that has been continuing since the past.
Now, let’s examine the given options-
Option a- ‘Will live’ is an incorrect option because we cannot use the future tense to indicate an action that began in the past.
Option b- ‘Lived’ is an incorrect option because we cannot use the past to indicate an action that is continuing in the present.
Option c- ‘Has been living’ is the correct option because we use the present perfect continuous tense to indicate actions that began in the past and is continuing in the present.
Option d- ‘Had been living’ is an incorrect option because we cannot use the past perfect continuous tense to indicate an action that is continuing.
The correct answer is Option ‘c’.

Note: The structure of present perfect continuous tense is; Subject + has/have + been + ing form of the verb + object. For example- She has been singing here for ten years.