Two vertical object pins are located on the principal axis of a thin lens at distances of $$x_{1}$$=  9.0cm and $$x_{2}$$= 18.0cm from the lens on the two sides of the lens. The images of the two pins formed by the lens are at the same position (overlap). The focal length and the nature of the lens are

A

15 $$\mathrm{cm}$$, convex

B

12 $$\mathrm{cm}$$, convex

C

15 $$\mathrm{cm}$$, concave

D

12 $$\mathrm{cm}$$, concave