A curved mirror produces an image that is three times the size of the object placed 20 cm apart. For the image to be real, the focal length of the mirror must be:

Magnification $= -\text{v}/\text{u}$

Then, $3 = -\text{v}/\text{u}$

Since the object is always placed on the left,

$u=-20cm$

The real image is also formed on the left side, 

$\text{v} = 3\text{u} = -60\text{cm}$

By mirror formula,

We get,

$\frac{1}{\text{f}} = \frac{1}{-20} + \frac{1}{-60}$

$\frac{1}{\text{f}} = \frac{3}{-60}+ \frac{1}{-60}$

$\frac{1}{\text{f}} = \frac{4}{-60}= \frac{1}{-15}$

$\text{f }= -15\text{cm }$