Question

how do jumman sheikh and alagu chowdhari maintain the dignity of their roles as judges in the story

Answer 1

Alagu Chowdhari without caring for his friendship with Jumman sheikh gives a true and just decision  against Jumman and in favour of the aunt, thus maintaining the dignity of his roles as the judge.
Similarily, Jumman Sheikh forgeting all the past happening and his enmity with Alagu Chowdhari gives a just decision.
In this way both of them maintain the dignity of their roles as judges

Answer 2

Algu chaudhary despite of his friendship with jumman, he took fair decision for aunt as the position of judge is the highest. When jumman got the chance to rule he release that the position of the judge is highest and no one can rule over it.... This way they managed their frienship