Given: $T_1 = 1200K, T_2 = T4 = 306K, Q_2 = 30kJ, Q_3 = 270kJ$
(Note: Here T2 and T4 represent the same temperature reservoir, but we use different notation so as to not confuse between the Engine sink and Heat pump sink)
![enter image description here](https://i.imgur.com/Z2cjYM1.png)
For Heat Engine, the Heat transfer is given by the ratio,
$\frac{Q_1}{Q_2} = \frac{T_1}{TT_2}$
$\frac{Q_1}{30} = \frac{1200}{306}$
$Q_1 = 177.647kJ$
Now, For Energy Balance of Heat Engine,
$W =Q_1 - Q_2$
W = 117.647 - 30 = 87.647kJ
Now, For Energy Balance of Heat Pump,
$Q_4 = W + Q_3$
$Q_4 = 87.647 + 270$
$Q_4 = 357.647kJ$
For Heat Pump, the Heat transfer is given by the ratio,
$\frac{Q_4}{Q_3} = \frac{T_4}{T_3}$
$\frac{357.647}{270} = \frac{306}{T_3}$
$T_3 = 231K = -42^oC$