How did Madhavrao Deshpande and Kakasaheb Dixit end up planning to travel to Shirdi together?

The meeting and travel plan between Madhavrao and Dixit was orchestrated by a series of chance encounters detailed in Chapter 51. Nanasaheb Panshe and Appasahib Gadre happened to see Madhavrao Balwant Deshpande and informed him that Kakasaheb Dixit was at Mirikar's house, very eager to go to Shirdi. They urged Madhavrao to go meet him. Madhavrao honored the request and went to Mirikar's house, where he was introduced to Dixit by Balasaheb. This was their very first meeting, and during this introduction, they clearly decided upon a plan to take the ten o'clock night train to Shirdi together.