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

$A$ Carnot engine $A$ working between temperatures $600 \ K$ and $T$ $(T < 600 \ K)$ and another Carnot engine $B$ working between temperatures $T$ $(T > 400 \ K)$ and $400 \ K$ are connected in series. If the work done by both the engines is the same, then $T =$ (in $K$)

Which statement is incorrect?

The efficiency of a Carnot engine is $\eta$ when its hot and cold reservoirs are maintained at temperatures $T_1$ and $T_2$,respectively. To increase the efficiency to $1.5 \eta$,the increase in temperature $(\Delta T)$ of the hot reservoir,while keeping the cold reservoir constant at $T_2$,is

$A$ reversible engine converts $1/6$ of its input heat into work. When the temperature of the sink is reduced by $62^{\circ}C$,the efficiency of the engine is doubled. Find the temperatures of the source and the sink.

$A$ Carnot engine operating between temperatures $7^{\circ}C$ and a higher temperature has an efficiency of $50\%$. To increase its efficiency to $70\%$,by how much must the temperature of the source be increased in $K$?