It is desired to concentrate an incoming solution of $3wt\%$ brine $($solution of salt and water$)$ to $5wt\%$ before sending to a crystallizer using a series of evaporators as shown in the Figure $1.$ Water leaving each evaporator is collected together to form Stream $8.$ Each evaporator removes the same quantity $($mass$)$ of water from its inlet solution. Assuming a suitable basis calculate at steady state,

F'igure $1$: $$vaporators in series

$($a$)$ The mass flow rate of the concentrated brine solution leaving evaporator $3($Stream $7)$

$($b$)$ The mass flow rate of water exiting each evaporator and Stream $8$

$($c$)$ The mass fraction of salt in the intermediate streams $($Streams $3$ and $5)$