Incandescent bulbs are designed by keeping in mind that the resistance of their filament increases with the increase in temperature. If at room temperature, $100 \mathrm{~W}, 60 \mathrm{~W}$ and 40 W bulbs have filament resistances $\mathrm{R}_{100}, \mathrm{R}_{60}$ and $\mathrm{R}_{40}$, respectively, the relation between these resistances is
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