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Three rods AB, BC and BD of same length l and cross section A are arranged as shown. The end D is immersed in ice whose mass is 440 g and is at `0^@C`. The end C is maintained at `100^@C`. Heat is supplied at constant rate of 200 cal/s. Thermal conductivities of AB, BC and BD are K, 2K and `K//2`, respectively Time after which whole ice will melt is (`K=100 cal//m-s^@C A=10cm^2,l=1cm`)

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