A concave mirror of focal length $10\text{cm}$ and a convex mirror of focal length $15\text{cm}$ are placed $40\text{cm}$ apart facing each other’s reflecting surface. A point object is placed between the mirror on their common axis and $15\text{cm}$ from the concave mirror. Find the position of images produced by reflection at concave mirror first and then at convex mirror.

The correct option is B $6\text{cm}$ behind the convex mirror

For mirror $M_1$, $O$ act as an object.
Let its image be $I_1$.
Then $u=-15\text{cm},f=-10\text{cm}$
$\Rightarrow \frac{1}{v}-\frac{1}{15}=\frac{1}{-10}\Rightarrow v=-30\text{cm}$
Image $I_1$ will act as an object for mirror $M_2$ its distance from mirror $M_2$
$u_1=-(40-30)\text{cm}=-10\text{cm}$
So $\frac{1}{v_1}+\frac{1}{u_1}=\frac{1}{f}\Rightarrow \frac{1}{v_1}+\frac{1}{-10}=\frac{1}{15}\Rightarrow v_1=+6\text{cm}$
Therefore, image $I_2$ is formed at a distance $6\text{cm}$ behind the convex mirror and is virtual.