Question $[25]$

A water flow of $108kgmol{H}_2\frac{O}{h}$ is employed to absorb $90\%$ of component $($A$)$ in a gas containing $1\mathrm{.}0$mol$\%$ of component $($A$)$ in air in a countercurrent stage tower. The total inlet gas flow to the tower is $30\mathrm{.}0$kgmo$\frac{l}{h}.$ The process takes place at $27CK$ at a total pressure of $1$atm. The equilibrium relation for component $($A$)$ in the gas$-$liquid is $y_A=2\mathrm{.}53x_A$

Determine the number of theoretical stages using the graphical method and the analytical Kremer equation.