How did Madhavrao Deshpande and Kakasaheb Dixit end up meeting and deciding to travel together?

Their meeting was a result of several fortunate coincidences detailed in chapter 51. Nanasaheb Panshe and Appasahib Gadre happened to see Madhavrao Deshpande and, knowing Kakasaheb Dixit was eager to go to Shirdi, they directed Madhavrao to go meet him at Mirikar's house. Madhavrao honored the request and went to meet Dixit as the sun was setting. Balasaheb Mirikar formally introduced the two men. This was their very first meeting, and during this introduction, they quickly made a firm plan to travel to Shirdi together on the ten o'clock night train. The news of Madhavrao's arrival brought great relief and satisfaction to Dixit, whose worries about his travel vanished.