A metal rod 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 evaporates and melts per unit time. If the point  ${ }^{\text{'}}{P}^{\text{'}}$  is at a distance of  ${ }^{\text{'}}\lambda x^{\text{'}}$ from the ice end. Then the value of  ${ }^{\text{'}}{\lambda }^{\text{'}}$  is 

 $(L_V$ of water $=540cal/g)$ $(L_f$ of ice $=80cal/g)$