The following parallel reactions take place in an isothermal, constant$-$volume CSTR:

$A-2B,-r_{A1}=k_1{C}_A,k_1=1\mathrm{.}3$min$-1$

$3A-C,-r_{A2}=k_2{C}_A,k_2=0\mathrm{.}4$min$-1$

Pure $A$ is fed to the reactor at a concentration of $250mo\frac{l}{m^3}.$

Determine the residence time $(,$ tau$)$ required to achieve $90\%$ conversion of species A under steady conditions.

A$.=2\mathrm{.}50$min

B$.=3\mathrm{.}00$min

C$.=2\mathrm{.}85$min

D$.=3\mathrm{.}60$min

E$.=3\mathrm{.}33$min