A concave mirror produces an image three times the size of an object placed 20 cm away. For a real image, the focal length should be

Magnification is given by:

$\text{M=-}\frac{\text{v}}{\text{u}}$, then $-3=-\frac{\text{v}}{\text{u}}$

The magnification of a concave mirror is always negative.

Where v is the image distance and u is the object distance.

$\text{u= -20cm}$

The object distance is always considered negative.

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

Mirror formula is given by:
$\frac{1}{f}=\frac{1}{v}+\frac{1}{u}$

Using the mirror formula, we get $\frac{1}{\text{f}}=\frac{1}{-20}+\frac{1}{-60}$

$\frac{1}{\text{f}}=\frac{3}{-60}+\frac{1}{-60}=\frac{4}{-60}=\frac{1}{-15}$

$\text{f=-15 cm}$