The relation of power ( watts ), applied voltage to the lamp in volts V and resistance R ( OHMS ) for a lamp is given by , P = V2/R , now assuming both lamps are working on same voltage ratings to get actual ratio of resistance so Voltage V is common operating condition,let us proceed to find ratio of resistances .

Suppose P1 , R1 and P2, R2 represents 0.50 w and 25 w lamps respectively , then their ratio equation is in terms of resistance is : R1/R2 = P2/P1 = 25 W/0.5 W =25 X 10 /5 = 50 , so 0.50 watts lamp will offer 50 times higher resistance than to 25 watts lamp

P=V^2/R or R=V^2/P. A .5 W bulb has more resistance than a 25 W bulb.

P = V2/R

For a given voltage, a 25W lamp has a resistance equal to V2/P

A 50W lamp would therefore has a resistance equal to V2/2P

Ratio 50w / 25w = (V2/2P) / (V2/P)

=0.5

i mean ratio