Answer
$15m$
Work Step by Step
Equating the intensity due to bulb 1 at a distance $r_1$ and the intensity due to bulb 2 at a distance $r_2$
$I_1=I_2$
$\implies \frac{P_1}{4\pi r_1^2}=\frac{P_2}{4\pi r_2^2}$
This simplifies to:
$r_1^2=\frac{P_1}{P_2}r_2^2$
$\implies r_1=r_2\sqrt{\frac{P_1}{P_2}}$
We plug in the known values to obtain:
$r_1=25\sqrt{\frac{45}{120}}$
$r_1=15$
