You are washing $1000$ ton$/$day of pulp. The wash water flow rate is $1400$ gal$/$min$.$ The consistency of the mat is $12\%.$ The consistency of pulp in the vat is $2\%.$ The concentrations of dissolved solids in the water phase in the vat and the leaving mat are $22\%$ and $9\%,$ respectively. The wash water going to this unit has dissolved solids of $5\%.$

a$)$ Calculate the wash factor.

b$)$ Calculate the dilution factor.

c$)$ Calculate the displacement ratio.

d$)$ Calculate the thickening factor.

e$)$ Calculate the efficiency of this stage.