1. Image formed by the convex lens alone

Given:

• Convex lens focal length: $f_L = +20\,\text{cm}$
• Object distance from lens: $u_L = -30\,\text{cm}$ (Cartesian sign convention)

Using the lens formula,

so,

Hence,

So the lens alone forms a real image $60\,\text{cm}$ to the right of the lens.

2. Position of this image relative to the concave mirror

The concave mirror is $80\,\text{cm}$ to the right of the lens.

Therefore, the image formed by the lens is at a distance

to the left of the mirror.

So for the mirror, this acts as an object placed at $20\,\text{cm}$ in front of it.

3. Use the condition in the question

The question says: the image remains at the same position even if the concave mirror is removed.

That means after reflection from the mirror and passing back through the lens, the final image is again formed at the same place as the lens-alone image, i.e. at $60\,\text{cm}$ to the right of the lens.

For this to happen most simply, the rays after reflection from the mirror must retrace their path through the lens. This occurs when the object for the concave mirror is at its center of curvature.

So the mirror must have:

Hence its focal length is

4. Maximum object distance for concave mirror alone to form a virtual image

A concave mirror forms a virtual image only when the object is placed between the pole and the focus.

Thus the maximum object distance for which it still forms a virtual image is equal to its focal length:

5. Check options

• A: $25\,\text{cm}$ ✗
• B: $10\,\text{cm}$ ✓
• C: $20\,\text{cm}$ ✗
• D: $30\,\text{cm}$ ✗

Therefore, the correct option is B.