In 1 ^ st case, Carnot engine operates between temperatures 300K...

The efficiency of a Carnot engine operating between two temperatures is given by $η = 1 - \dfrac{{T}_{L}}{{T}_{H}}$

For the first case : $η = 1 - \dfrac{100}{300} = \dfrac{2}{3}$

For the second case : ${η}_{net} = {η}_{1} + {η}_{2} - {η}_{1}{η}_{2}$

${η}_{1} = 1 - \dfrac{200}{300} = \dfrac{1}{3}$

${η}_{2} = 1 - \dfrac{100}{200} = \dfrac{1}{2}$

${η}_{net} = \dfrac{1}{3} + \dfrac{1}{2} - \dfrac{1}{6} = \dfrac{2}{3}$

$η$(first case)$= η$(second case)