A metal rod AB of length 10x has its one end A in ice at 0 C, and the other end B in water at 100 C. If a point P one the rod is maintained at 400 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 540cal/g and latent heat of melting of ice is 80cal/g. If the point P is at a distance of lambda x from the ice end A, find the value lambda. [Neglect any heat loss to the surrounding.]