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A metal rod AB of length 10x has its one...

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 `1000^@C`. If a point P on the rod is maintained at `400^@C`, then it is fouund 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 `lambdax` from the ice end A, find the value of `lambda`. (Neglect any heat loss to the surrounding).

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