Mrs. Pearson and Mrs. Fitzgerald, the two main characters in the story "The Fun They Had" by Isaac Asimov, go back to their original selves when the situation goes out of hand. Let's analyze this in detail:

1. Background of the Story:
- The story is set in the future where education is provided through mechanical teachers and children rarely interact with each other.
- Tommy, a young boy, finds an old book in his attic, which describes how children used to go to school together and have real teachers.
- Tommy and Margie, his neighbor and fellow student, discuss how different their education system is compared to the past.

2. Mrs. Pearson and Mrs. Fitzgerald:
- In the story, Mrs. Pearson and Mrs. Fitzgerald are the mechanical teachers of Tommy and Margie, respectively.
- They are programmed to teach and interact with the children, but they lack the personal touch and warmth of human teachers.

3. When Mrs. Pearson's Family Gets to Know About Them:
- This option is not correct because Mrs. Pearson's family does not play a significant role in the story.
- The story primarily focuses on the children's perspective and their thoughts on the educational system.

4. When They Both Get Bored:
- This option is also not correct because there is no indication in the story that Mrs. Pearson and Mrs. Fitzgerald can get bored.
- They are programmed machines designed to teach, and their behavior is not influenced by emotions.

5. When the Situation Goes Out of Hand:
- This is the correct answer because towards the end of the story, the situation with the mechanical teachers becomes chaotic.
- Tommy and Margie mention that the mechanical teachers sometimes get the answers wrong or give them more difficult questions than they can handle.
- This creates frustration and dissatisfaction among the children, leading to a desire for a change in the educational system.

6. None of the Above:
- This option is incorrect because, as explained earlier, the correct answer is "C" - When the situation goes out of hand.

In conclusion, Mrs. Pearson and Mrs. Fitzgerald go back to their original selves when the situation with the mechanical teachers becomes unmanageable and chaotic, causing the children to desire a different form of education.