Three air streams meet to form a common main return air stream of $1550\frac{m^3}{m}in.$ The initial air streams contain $CH4$ as follows$-$

$($a$)300\frac{m^3}{m}in-$ No methane

$($b$)650\frac{m^3}{m}in-0\mathrm{.}7\%CH4$

$($c$)600\frac{m^3}{m}in-1\mathrm{.}1\%CH4$

In addition, there is an emission in the main return airway of $2\mathrm{.}5m^3$ of pure methane per minute. Calculate$-$

$($i$)$ Final concentration of $CH4$ in the return airway assuming perfect mixing.

$($ii$)$ Volume required from airway $($a$)$ to reduce the $f$ nal $CH4$ concentration by $30\%$ assuming other quantities are not changed