Even if the generation of bacteria was smaller, older or if the infection was going on for a long time, the antibiotics should be able to treat both infections, as its action does not depend on the amount or age of the bacteria. Therefore, A and C are both incorrect.
Rare genetic conditions usually appears in other members of the family as well. And there is no indication of the genetic condition. So D is wrong too.
The most reasonable explanation would be that the bacteria developed the ability to kill the drugs designed to kill them. As they are from the same family, it is possible that K was infected with the offspring of the bacterias in X. Therefore, the correct answer is B. The generation of S. agalactiae responsible for the second infection descended from bacteria that were selected for their resistance to tetracycline.