Final answer:
The narrator's interest in Mangan's sister is real and reciprocated to some extent.
Step-by-step explanation:
In the given passage, the narrator's interest in Mangan's sister and her interest in him can be inferred through their actions and thoughts. The narrator is shown to have a strong fascination with Mangan's sister, as he thinks about her often and keeps a memento of her. He also feels tormented by his feelings for her. On the other hand, the narrator's interest in him is not explicitly stated in the passage, but it can be understood that Mangan's sister reciprocates his feelings to some extent, as she is shown to be aware of his presence and reacts to his attention. Therefore, it can be concluded that the narrator's interest in Mangan's sister is real and not imagined.