Gas phase decomposition of A in a CSTR is irreversible;

$AB+C+2D$

The above$-$reaction obeys the rate$-$equation:

$r=\frac{k{C}_A}{1+K_A{C}_A}$

The value of $k$ is $45h{r}^{-1}$ and the value of $K_A$ is $50$ lit$/$mole $A.$ The volume of the reactor is $1000$ liter and the molar feed rate of A to the CSTR is $500$ moles$/$hr$.$ The reactor operates at $400K$ and $1$atm total pressure. The mole fraction of $A$ in the feed

s $0\mathrm{.}5.$ The feed mixture consists of A and inert.

What is the fractional conversion of $A$ in the stream leaving the CSTR$?$