Two Carnot engines A and B are operated in series. Engine A receives heat from a reservoir at 600 K and rejects heat to a reservoir at temperature T.…

Two Carnot engines A and B are operated in series. Engine A receives heat from a reservoir at $\displaystyle 600$ K and rejects heat to a reservoir at temperature T. Engine B receives heat rejected by engine A and in turn rejects it to a reservoir at $\displaystyle 100$ K. If the efficiencies of the two engines A and B are represented by $\displaystyle \eta_A$ and $\displaystyle \eta_B$, respectively, then what is the value of $\displaystyle \frac{\eta_{\mathrm{B}}}{\eta_{\mathrm{A}}}$ ?