A verb is used to express an occurrence, action, or state. It is the grammatical center of the predicate in a sentence.

An auxiliary verb is a verb which gives is used in the formation of tenses, moods, tones, etc.

Option A is correct as interested indicates the use of simple past tense. Hence, we must use the helping verb was (the subject 'neither of them' is singular)

The other options are wrong as no other tense can be used here.

The correct answer is A)was