If a 100 cubic feet atmospheric air at zero degree fahrenheit were compressed to a volume of 1 cubic feet at a temperature of 200 °F, what will be the pressure of air ?

Assuming it started out at 1 atm pressure, then

PV=kT, so you want P such that
P/K(200) = 100/K(0)
where K(F) = 5/9 (F-32) + 273