A spherical mirror forms an erect image three times the size of the object. If the distance between the object and the image is 80$cm$, the nature and the focal length of the mirror are

Magnified image is formed only by concave mirror. But this image may be real or virtual.

For real image,

 $$\begin{gathered} 2x=80cm \\ \therefore x=40cm \end{gathered}$$

$\frac{1}{-120}+\frac{1}{-40}=\frac{1}{f}$

Solving, we get $f=-30cm$

Similarly, we can check for virtual image.