IIT JEE Advanced 2009 Paper 2

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 on 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 540 cal/g and latent heat of melting of ice is 80 cal/g. If the point P is at a distance of l x from the ice end A, find the value of l. (Neglect any heat loss to the surrounding.)