An object is placed at a distance of $20\text{cm}$ from a concave mirror and its real image is formed at distance of $20\text{cm}$ from the mirror. The focal length of mirror is

The correct option is B $10\text{cm}$
For a real image, when object distance = image distance = $20\text{cm}$
$\Rightarrow$ It means object is placed at centre of curvature of concave mirror.
$R=20\text{cm}$
$2f=20\text{cm}$
$f=\frac{20}{2}=10\text{cm}$
So the focal length is $10\text{cm}$

Why this question? For spherical mirrors whose aperture is much smaller than its radius of curvature, we use $R=2f$.