When two bulbes with 25W and 100W rated at 220V are connected in series with a supply of 440V which will fuse?

The 25w bulb, since it has the much higher resistance.

The resistance can be derived from:

P = V^2/R

R = V^2/P

For the 100w bulb:

R = 220^2/100 = 484 ohms

For the 25w bulb:

R = 220^2/25 = 1936 ohms

When connected in series, and then connected to 440V, the voltage across the 100w bulb would be:

V = 440*484/(484+1936) = 88V

This is well within spec.

The voltage across the 25w bulb would be:

V = 440*1936/(484+1936) = 352v

This is way over spec, and would cause the bulb to fuse.

Although this answer assumes that a light bulb is a linear resistor, they are not. The resistance of a light bulb changes significantly with voltage and filiament temperature. The 25w light bulb is still the one that fuses, but the non-linearity of the resistance needs to be understood.