The efficiency of a Carnot engine operating between reservoirs maintained at temperatures $27^{\circ}C$ and $-123^{\circ}C$ is ...... $\%$

$A$ reversible engine converts one-sixth of the heat supplied into work. When the temperature of the sink is reduced by $62^{\circ} C$,the efficiency of the engine is doubled. The temperatures of the source and sink are

This question has Statement $1$ and Statement $2.$ Of the four choices given after the Statements,choose the one that best describes the two Statements.
Statement $1 :$ An inventor claims to have constructed an engine that has an efficiency of $30\%$ when operated between the boiling and freezing points of water. This is not possible.
Statement $2:$ The efficiency of a real engine is always less than the efficiency of a Carnot engine operating between the same two temperatures.

Under which ideal condition does the efficiency of a Carnot engine become $100 \%$?

Three designs are proposed for an engine which is to operate between $500 \ K$ and $300 \ K$. Design $A$ claims to produce $150 \ J$ of work per $1000 \ J$ of heat input, design $B$ $450 \ J$ of work per $1000 \ J$, and design $C$ $300 \ J$ of work per $1000 \ J$. Which of the designs would you choose?

In a heat engine,the temperature of the source and sink are $500\, K$ and $375\, K$. If the engine consumes $25\times10^5\, J$ per cycle,the work done per cycle is