Two metal rods A and B of equal lengths and equal cross-sectional areas are joined end to end. The coefficients of thermal conductivities of A and B are in the ratio 2:3, when the free end of A is maintained at $100^{\circ}C$ and the free end of B is maintained at $0^{\circ}C$, the temperature of the junction is :

Question

( A ) $60^{\circ}C$
( B ) $30^{\circ}C$
( C ) $40^{\circ}C$
( D ) $50^{\circ}C$