Answer
a) $A$: $29 \% \hspace{2mm}$ $B$: $38 \% \hspace{3mm}$ $C:54 \% \hspace{3mm}$ $D:24 \%$
b) Claimed efficiency of $C$ is impossible.
c) Decreasing order : $B>D>A$
We make this table first:
Work Step by Step
The maximum possible efficiency is that of a Carnot engine.
a) $A$:
Maximum efficiency $=1-\dfrac{320.15}{450.15}\simeq 0.29 \equiv29 \%$
$B$:
Maximum efficiency $=1-\dfrac{290.15}{470.15}\simeq 0.38 \equiv 38 \%$
$C$:
Maximum efficiency $=1-\dfrac{240.15}{520.15} \simeq 0.54 \equiv 54 \%$
$D$:
Maximum efficiency $=1-\dfrac{310.15}{410.15}\simeq 0.24 \equiv 24 \%$
b) The claimed efficiencies must always be less than the Carnot efficiency. Here, the claimed efficiency of prototype $C$ is greater than the corresponding Carnot efficiency. Thus, this claim is impossible. All others are fine.
c) Ratio for $A$ $=\dfrac{21}{29} \simeq 0.72$
Ratio for $B$ $=\dfrac{35}{38}\simeq 0.92$
Ratio for $D$ $=\dfrac{20}{24}\simeq 0.83$
Decreasing order:
$B>D>A$
