Question

what did the old pilgrim have no need to build the bridge across the chasm?​

Answer 1

Answer: The old man had already crossed the river. So there was no need for him to repair the broken bridge across the chasm. He could have easily went on to the other side without bothering about who comes next.

But the old man showed deep sense of humanity understanding that the next passerby would suffer because of the broken bridge. Without any selfish reasons he repaired the broken bridge for others who would come after him.