A converging lens which has a focal length of 20 cm is placed 60 cm to the left of a concave mirror of focal length 30 cm. An object is placed 40 cm to the left of lens. The position of the final image is:

60 cm

For refraction through the lens

u = −40 cm, f = + 20 cm

Lens equation is : $\frac{1}{v}-\frac{1}{u}=\frac{1}{f}$ or $\frac{1}{v}-\frac{1}{-40}=\frac{1}{20}$ or $\frac{1}{v}=\frac{1}{20}-\frac{1}{40}$

or v = +40 cm

This gives the position of image $I_1$. Image $I_1$ will be a real inverted image formed at 40 cm to the right of the lens. As concave mirror is placed to the right of lens at 60 cm, hence the image $I_1$ is at a distance of 20 cm from the mirror. Therefore, image $I_1$ becomes a real object for the concave mirror. 

For reflection by concave mirror :

The position of the object $I_1$ is within the focal length of the concave mirror

Here, u = −20 cm, f = −30 cm

Mirror formula is : $\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$ or $\frac{1}{v}-\frac{1}{20}=-\frac{1}{30}$

or $\frac{1}{v}=\frac{1}{20}-\frac{1}{30}=\frac{1}{60}$ or v = +60 cm

This gives the position of final image I.