Answer:
Let \[{{K}_{1}}\] and \[{{K}_{2}}\] be the coefficients of thermal conductivity of the materials and \[{{t}_{1}}\] and \[{{t}_{2}}\] be the times in which ice melts in the two vessels. As the same quantity of ice melts in the two vessels, the quantity of heat flowed into the vessels must be same. \[\therefore \] \[Q=\frac{{{K}_{1}}A({{T}_{1}}-{{T}_{2}}){{t}_{1}}}{x}=\frac{{{K}_{2}}A({{T}_{1}}-{{T}_{2}}){{t}_{2}}}{x}\] or \[{{K}_{1}}{{t}_{1}}={{K}_{2}}{{t}_{2}}\] \[\therefore \] \[\frac{{{K}_{1}}}{{{K}_{2}}}=\frac{{{t}_{2}}}{{{t}_{1}}}=\frac{25\min }{10\min }=\mathbf{5:2}.\]
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