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 $T$. Engine $B$ receives; heat rejected by engine $A$ and in turn rejects it to a reservoir at $100\,K$. If the efficiencies of the two engines $A$ and $B$ are represented by ${\eta _A}$ and ${\eta _B}$ respectively, then what is the value of $\frac{{{\eta _A}}}{{{\eta _B}}}$
  • A$\frac{{12}}{7}$
  • B$\frac{{12}}{5}$
  • C$\frac{{5}}{12}$
  • D$\frac{{7}}{12}$
JEE MAIN 2018, Diffcult
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