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

Image is magnified, so mirror is concave because convex mirror always makes diminished image. Further, image is erect and magnified. So, the object lies between P and F and its image is virtual.

4x = 80cm $\Rightarrow$x = 20cm and 3x = 60cm
Applying the mirror formula, $\frac{1}{f}=\frac{1}{v}+\frac{1}{u}=\frac{1}{+60}+\frac{1}{-20}\Rightarrow$ f = -30cm