What is the chemical formula of permutit and how it is used?

Hi Kumar Gaurav!

Permutit is a complex inorganic salt having the formula Na₂Al₂Si₂O₈.xH₂O. It is also known as sodium-aluminium silicate or zeolites.

It is used in the ion exchange method for softening hard water. The Permutit is packed loosely in a big tank over a layer of coarse sand. From the top hard water is introduced into the tank which reaches the bottom and then rises through the layer of the Permutit. The cations present in hard water are exchanged for sodium ions. 

Hope, this answer helps.

Cheers!