We can solve the problem by using the mirror equation:
[tex] \frac{1}{f} = \frac{1}{d_o}+ \frac{1}{d_i} [/tex]
where
f is the focal length
[tex]d_o[/tex] is the distance of the object from the mirror
[tex]d_i[/tex] is the distance of the image from the mirror
For the sign convention, the focal length is taken as negative for a convex mirror:
[tex]f=-120 cm[/tex]
and the image is behind the mirror, so virtual, therefore its sign is negative as well:
[tex]d_i=-24 cm[/tex]
putting the numbers in the mirror equation, we find the distance of the object from the mirror surface:
[tex] \frac{1}{d_o} = \frac{1}{f}- \frac{1}{d_i}= \frac{1}{-120 cm} - \frac{1}{-24 cm}= \frac{1}{30 cm} [/tex]
So, the distance of the object from the mirror is [tex]d_o = 30 cm[/tex]
