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 and ice 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.)