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My Solution:

I took the current to be same as the bulbs are connected in series.

As the current will be the same in each bulb, I took the current as 'i'

P=V*i

For bulb with power 60W

60=v*i

v=60/i

For bulb with power 40W

40=V*i

V=40/i

Adding V and v

V+v=220

40/i + 60/i = 220

100/i = 220

i = 100/220 = 10/22 = 5/11

Then I calculated the resistance by using the formula P=i^2 * r

Have I done the question correctly?

If no, then please point out the mistake