\(\frac{1}{ v }-\frac{1}{ u }=\frac{1}{ f }\)

\(\Rightarrow \frac{1}{ v }-\frac{1}{(-60)}=\frac{1}{20} \Rightarrow \frac{1}{ v }+\frac{1}{60}=\frac{1}{20}\)

\(v =30\,cm\)

For final image to be formed on the objectitself, after refraction from lens the ray should meet the mirror perpendicularly and the image by lens should be on the centre of curvature of mirror

\(R =30-10=20\,cm\)

Focal length of mirror \(= R / 2=10\,cm\)