Answer
At $100~W$, the current passes through the filament with the larger resistance
At $200~W$, the current passes through the filament with the smaller resistance
At $300~W$, the current passes through the filaments wired in parallel
Work Step by Step
We can write an expression for the power:
$P = \frac{V^2}{R}$
At $100~W$, the current passes through the filament with the larger resistance
At $200~W$, the current passes through the filament with the smaller resistance
At $300~W$, the current passes through the filaments wired in parallel