Final answer:
A. on. The correct preposition to complete the sentence is 'on'.
Step-by-step explanation:
In this sentence, the correct preposition to complete it is on. Ms. Jordan was on duty during lunch. The word 'on' is used to indicate that someone is performing a duty at a specific time or during a specific period. For example, you can say 'on duty' to describe someone who is working or responsible for something at a particular time.