In Carnot engine efficiency is 40 \% at hot reservoir temperature T...

The efficiency of a heat engine is defined as the ratio of work done to the heat supplied, ie, $\eta=\frac{\text{ Work done }}{\text{ Heat input }}=\frac{W}{Q}$ or $\quad \eta=1-\frac{T_2}{T_1}$ where $T_2$ is temperature of sink, and $T_1$ is temperature of hot reservoir $\therefore \quad \frac{40}{100}=1-\frac{T_2}{T_1} \Rightarrow \quad \frac{T_2}{T_1}=0.6 \Rightarrow \quad T_1=0.6 T_1$ Again, $\quad \frac{50}{100}=1-\frac{T_2}{T_1^{\prime \prime}} \Rightarrow \quad \frac{T_2}{T_1{ }^{\prime}}=0.5$$\begin{array}{ll}\Rightarrow & \frac{0.6 T_1}{T_1{ }^{\prime}}=0.5 \\ \therefore & T_1{ }^{\prime}=\frac{0.6}{0.5} T_1=\frac{6}{5} T\end{array}$$$