Two different rods $A$ and $B$ are kept as shown in figure. The variation of temperature of different cross sections is plotted in a graph shown in figure. The ratio of thermal conductivities of $A$ and $B$ is
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$\because\left(\frac{\Delta \mathrm{Q}}{\Delta \mathrm{t}}\right)_{\mathrm{A}}=\left(\frac{\Delta \mathrm{Q}}{\Delta \mathrm{t}}\right)_{\mathrm{B}} \quad \therefore \frac{\mathrm{K}_{\mathrm{A}} \mathrm{A}(100-70)}{30}$
$=\frac{\mathrm{K}_{\mathrm{B}} \mathrm{A}(70-35)}{70} \Rightarrow \mathrm{KA}=\frac{\mathrm{K}_{\mathrm{B}}}{2} \Rightarrow \frac{\mathrm{K}_{\mathrm{A}}}{\mathrm{K}_{\mathrm{B}}}=\frac{1}{2}$
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