The evaporation capacity of a descending film evaporator is $15kg$ water$/$h$.$ Such a system consists essentially of a heating unit which heats a liquid flowing in the form of a film, and a condenser in which the water vapor generated in this process is condensed. Evaporation occurs when a liquid at its boiling point undergoes to low$-$pressure unit from high pressure unit. This event is called "flashing" $($sudden evaporation$).$ A portion of the resulting concentrate is recycled to the evaporator by mixing with the feed through a recycle $($circulation$)$ pump. The capacity of the recycle pump is $30k\frac{g}{h}.$ The feed contains $6\%$ and the concentrate contains $32\%$ dry matter. According to this,

a$)$ The feed mass flow rate,

b$)$ Concentrated production rate,

c$)$ Recycle mass flow rate,

d$)$ Calculate the dry matter content in the recycled stream