A metal rod `AB` of length `10x` has it one end 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 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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Explanation

`(dm_(ice))/(dt) = (dm_(vapour))/(dt) , (400KS)/(lambdaxL_(ice)) = (300KS)/((10-lambda)xL_(vapour))`
`(400)/(lambdaxx80) = (300)/((10-lambda)540) = lambda=9` .