Potential remains same in the resistors when they are connected in the parallel.∴ Potential in both the bulbs will be same.
Now,
For First Tungsten Bulb,
Power=100W.
Potential=220V.
Power=Potential∗Current.
Current=100220
Current=0.45A.
For second Tungsten bulbs,
Power =60W.
Potential =220V.
Current =60220=0.27A.
Now, Total current flowing = Current in 1st bulb + Current in 2nd bulb.=0.45+0.27=0.72A.
Hence, the total current flowing in the main conductor is 0.72A.