A reverse osmosis $($RO$)$ system, as shown in Figure Q$1,$ is used for desalination of brackish water to produce drinking water. The feedwater contains total dissolved solid $($TDS$)$ of $2,000m\frac{g}{L}.$ The feed to the RO system has a flowrate of $100\frac{m^3}{d}.$ Stage $1$ has water recovery of $45\%.$ Assume the concentration polarization factor is $1\mathrm{.}2$ in all stages. All the permeates from Stage$-1$ and Stage$-2$ are blended to make the final product water. All the RO membranes used in the system have intrinsic rejection of $98\%$ for TDS$.$ The temperature is at $20C.$ Determine the maximum water recovery of Stage$-2$ to meet the requirement of final product water with TDS $80m\frac{g}{?}.$ State all assumptions made.

$(12$ Marks$)$