A metal rod AB of length 10x has its one end A in ice at $$0^\circ C$$ and the other end B in water at $$100^\circ C$$. If a point P on the rod is maintained at $$400^\circ C$$, then it is found that equal amounts of water andice evaporate and melt per unit time. The latent heat of evaporation of water is 540 cal/g and latent heat of melting of ice is 80 cal/g. If the point P is at a distance of $$\lambda x$$ from the ice end A, find the value of $$\lambda$$. [Neglect any heat loss to the surrounding.]