An object is placed at a distance of $20cm$ from the pole of a concave mirror of focal length $10cm$. The distance of the image formed is:

The image created by this mirror depends on the initial position of the object, if the position of the object varies then the image of the same object may be different.
The fixed formula of the concave mirror is 

$\frac{1}{f}=\frac{1}{v}+\frac{1}{u}$

 we use the symbol agreement here.
In the given question, the object is placed in front of the mirror, the object's distance is considered negative and the approximate length of the concave mirror is negative, so
⇒$\frac{1}{v}+\frac{1}{-20}=\frac{-1}{10}$

⇒$\frac{1}{v}=\frac{-1}{10}+\frac{1}{20}=\frac{(-2+1)}{20}=\frac{-1}{20}$

$v=-20cm$, which is why the image of the object is 20cm from the fixed pole of the curved mirror.
Thus, the correct answer is Option C.