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 $\frac{{{\eta _A}}}{{{\eta _B}}}$
JEE MAIN 2018, Diffcult
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Efficiency of engine $A,{n_A} = \frac{{{T_1} - {T_2}}}{{{T_1}}}$
and ${n_B} = \frac{{{T_2} - {T_3}}}{{{T_2}}};{T_2} = \frac{{{T_1} + {T_3}}}{2} = 350\,K$
$or\frac{{{n_A}}}{{{n_B}}} = \frac{{\frac{{600 - 350}}{{600}}}}{{\frac{{350 - 100}}{{350}}}} = \frac{7}{{12}}$
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