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

The meeting between Madhavrao Deshpande and Kakasaheb Dixit was a result of a series of fortunate events described in Chapter 51. Nanasahib Panshe and Appasahib Gadre happened to see Madhavrao and, knowing Dixit was eager to go to Shirdi, directed Madhavrao to Mirikar’s house. They believed Madhavrao was the perfect person to accompany Dixit. At the house, Balasaheb formally introduced the two men. They quickly made a plan to travel together on the ten o'clock night train. This meeting was crucial, as it alleviated Dixit's worries and set the stage for their joint journey, which began later that evening after they took Baba's portrait with them.