A convex lens and convex mirror are separated by distance ‘d’ as shown in the figure the minimum value of ‘d’ so that image formed on the object it self (in cm)

If the final image is coinciding with the object, the image formed by the lens is at the centre of curvature of the spherical mirror.

$\frac{1}{\mathrm{f}}=\frac{1}{\mathrm{v}}-\frac{1}{\mathrm{u}}\Rightarrow \frac{1}{10}-\frac{1}{15}=\frac{1}{\mathrm{v}}\Rightarrow \mathrm{v}=30\mathrm{cm}$

So the image formed by the lens will be at at a distance of 20cm from the mirror. hence the distance between the lens and mirror will be 10cm.