For which combination of working temperatures is the efficiency of a Carnot engine the highest?

$A$ heat engine receives $200 \, cal$ of heat and rejects $150 \, cal$ of heat. If the temperature of the source is $400 \, K$,what is the temperature of the sink in $K$ (in $, K$)?

The source temperature of a heat engine is $727^{\circ}C$ and the sink temperature is $227^{\circ}C$. What is the maximum possible efficiency of this engine?

The efficiency of a Carnot engine is $50 \%$ when the temperature of the sink is $500 \ K$. If the efficiency of the Carnot engine is to be increased to $60 \%$,what should be the temperature of the sink,keeping the temperature of the source constant (in $K$)?

Two Carnot engines $A$ and $B$ operate in series such that engine $A$ absorbs heat $Q_1$ at temperature $T_1$ and rejects heat $Q$ to a sink at temperature $T$. Engine $B$ absorbs half of the heat rejected by engine $A$ (i.e.,$Q/2$) and rejects heat $Q_3$ to the sink at temperature $T_3$. When the work done in both cases is equal,the value of $T$ is:

$A$ Carnot engine has the same efficiency between $(i)$ $100 \ K$ and $600 \ K$ and (ii) $T \ K$ and $960 \ K$. The temperature $T$ in kelvin of the sink is