B

Step 1: For a convex lens, the image formed can be described using the lens formula:
$$ \frac{1}{f} = \frac{1}{v} - \frac{1}{u} $$
where:
- $f$ is the focal length of the lens
- $v$ is the image distance from the lens
- $u$ is the object distance, and it is taken as negative according to the sign convention.

Step 2: From the question, it mentions that the object is placed at two distances, and both produce the same size images. This condition occurs when the object distance $u$ is at $f$ and $v = 2f$, or at $2f$ and $v = f$.

Step 3: If we assume the values for $u$ to be 20 cm (the second case, where $u = -20$ cm gives the same image size as saying it is at 10 cm from the lens) and 10 cm, leading to $u = -10$ cm.
Therefore:
For case 1, if $u = -20$ cm:
$$ v = 2f \Rightarrow f = 20 \text{ cm} $$
For case 2, if $u = -10$ cm:
$$ v = f \Rightarrow f = 10 \text{ cm} $$

Therefore the focal length that fits this requirement is 10 cm.
Hence the correct focal length of the convex lens is 10 cm. Therefore, option B is correct.