JEE Main 2020 — Thermodynamics Question with Solution

Two ideal Carnot engines operate in cascade (all heat given up by one engine is used by the other engine to produce work) between temperatures, ${\mathrm{T}}_1$ and ${\mathrm{T}}_2$ . The temperature of the hot reservoir of the first engine is ${\mathrm{T}}_1$ and the temperature of the cold reservoir of the second engine is ${\mathrm{T}}_2$ . $\mathrm{T}$ is temperature of the sink of first engine which is also the source for the second engine. How is $\mathrm{T}$ related to ${\mathrm{T}}_1$ and ${\mathrm{T}}_2$ , if both the engines perform equal amount of work?