A man A reaches the first floor by staircase whereas the man B uses escalator to reach the first floor from the ground floor. Both have same mass. The work done by both the people is equal I.e. Mgh . But work is a path function it depends on the path being followed . Then why is the work done in above two cases equal mgh? How?

The work done on the two people is the same - as you say it's equal to mgh. But the work done by the two people is different - man A expends mgh amount of energy, and Man B expends no energy (the energy mgh is expended by the escalator machinery, not by Man B).

You say that work is a "path function" - but actually it's a scalar quantity equal to the dot product of the force being overcome and path traveled:



In the case of work against gravity all that matters in determining the work expended is the vertical distance covered. So climbing up a vertical rope 10 meters high requires the same amount of work as walking up a gentle incline that rises 10 meters over a 100 meter length.