Two rods of identical cross-section A and length L have thermal conductivities k and 2k. They are joined end to end and their free ends are held at…

Thermal resistances add in series: $R_1=L/(kA)$ and $R_2=L/(2kA)$, so $R_{tot}=\dfrac{3L}{2kA}$. A single rod of length $2L$ with the same resistance has $k_{eq}=\dfrac{2L}{AR_{tot}}=\dfrac{4k}{3}$; A is true. The temperature drop across each rod is proportional to its resistance, so the drop across the rod of conductivity $2k$ is $100\times\dfrac{1/2}{3/2}=33.3^\circ$, which is the junction temperature, not $66.7^\circ$; B is false. In parallel the conductance is $(k+2k)A/L=3kA/L$, while in series it is $\dfrac{2kA}{3L}$, a ratio of $4.5$; C is true. The same heat current flows through both rods, so the gradient is inversely proportional to conductivity: it is twice as large in the rod of conductivity $k$, not in the $2k$ rod; D is false.