230V*Iac = 200W = n*12V*Idc
where n is the efficiency
assuming 50% efficiency in the inverter,
Idc = 200/(0.5*12)
= 34A
to run for 1 hour --> need 34Ah battery
to run for 10 hour --> need 340Ah battery
assuming you only discharge half of the battery (for lifetime concerns)
battery...