$(35$ points$)$ The irreversible elementary gas phase reaction

$2AB+C$

is currently carried out in a packed bed reactor containing $100kg$ of catalyst. The entering

pressure is $20$atm and the exit pressure is $4$atm. Currently $50\%$ conversion is achieved. It is

proposed to add a CSTR with $200Kg$ of catalyst downstream of the PBR$.$ There is no pressure

drop in the CSTR$.$ The flow rate and temperature remain unchanged.

What would be the overall conversion in such an arrangement?