first of all, given is so vague that complete rating of the bulb was not mentioned. it is essential that voltage rating ( or current) of the bulb be clearly stated. for the sake of discussion, let us say that each bulb are rated 60W and 100W and 240V each..
calculating the rated resistance of each lamp using P = V2
/R, we can calculate the resistance of the 60W lamp as 960 ohms and resistance of the 100W lamp as 576 ohms.
so when they are connected in series across a 240V source, total resistance would be equal to 1536 ohms giving a current ( I = V/R) of 0.1563 ampere.
getting again the power consumed by each lamp when connected in series across a 240V source using I2
R formula, the power across 60W lamp will now be 23.42 watts only while the power on the 100W lamp is 14.05 watts only.
considering the setup, the 60W lamp will glow brighter than the 100W lamp.
it would arrive into a different answer when configurations where known and altered like:
1. bulbs are rated 120V only
2. 1st bulb is 120V and another bulb is 240V
3. or author is thinking of a given like 60Ω and 100Ω rather than 60W and 100W where in this case the 100Ω bulb will consume 225Watts while 60Ω is 135 watts only, thus 100Ω is brighter.