JEE Main 2018 — Thermodynamics Question with Solution

Two Carnot engines $\mathrm{A}$ and $\mathrm{B}$ are operated in series. Engine A receives heat from a reservoir at $600\mathrm{K}$ 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 $100\mathrm{K}$. If the efficiencies of the two engines $\mathrm{A}$ and $\mathrm{B}$ are represented by ${\eta }_A$ and ${\eta }_B$ respectively, then what is the value of $\frac{{\eta }_{\mathrm{A}}}{{\eta }_{\mathrm{B}}}$