Explanation

(a) $\eta = 1 - \frac{T_{2}}{T_{1}}\ \Rightarrow \frac{T_{2}}{T_{1}} = 1 - 2\eta = 1 - \frac{1}{6} = \frac{5}{6}$ …(i)
in second case $\frac{T_{2} - 62}{T_{1}} = 1 - \eta^{'} = 1 - \frac{2}{6} = \frac{2}{3}$ …(ii)
from Eqs. (i) and (ii)
now $T_{2} - 62 = \frac{2}{3}T_{1} = \frac{2}{3} \times \frac{6}{5}\ T_{2}$
$\Rightarrow \ \ T_{2} = 310\ K = 310 - 273 = 37℃$
$T_{1} = \frac{6}{5}\ T_{2} = \frac{6}{5}\ \times 310 = 372\ K = 372 - 273 = 99℃$