All 4 stages span a total of 4 weeks or 28 days.
Egg - 2 days
Larva - 7 days
Pupa - 5 days
Adult - 14 days
This means that the larva exists for 7/28 = 25% of the time.
So, 25% of the randomly selected developing bees would be larva.
25% of 200 is 50. So, the answer is A.
Edit: The question is ambiguous. If by developing bees they exclude all the adult bees, then larva exist for 50% of the time and the answer would be 100.