15a. Neither the mayor nor the council members have filed their reports.
15b. Neither the mayor nor the council members have filed his reports.
my answer is A. what's the rationale please?
A is correct.
The choice is between the word "their" or "his" - after the conjunction "nor" (works with "or" too).
When using either of these conjunctions, the noun that is closer to the verb and the pronoun is what governs the choice. Since "council members" is closer to the verb and the pronoun, you need to use the plural - "their."