Step 1: Efficiency of a Carnot Engine
The efficiency of a Carnot engine is given by:
\[
\eta = 1 - \frac{T_C}{T_H}
\]
where:
- \( T_H \) is the temperature of the hot reservoir,
- \( T_C \) is the temperature of the cold reservoir.
Step 2: Relating Work to Heat Input
In isothermal expansion, the heat absorbed \( Q_H \) is proportional to the work done \( W_H \):
\[
Q_H = W_H
\]
Similarly, in isothermal compression:
\[
Q_C = W_C
\]
Given:
\[
W_H = 1.25 W_C
\]
Using efficiency definition:
\[
\eta = \frac{W_H - W_C}{W_H}
\]
\[
\eta = \frac{1.25 W_C - W_C}{1.25 W_C}
\]
\[
\eta = \frac{0.25 W_C}{1.25 W_C} = \frac{0.25}{1.25} = 0.2
\]
\[
\eta = 20%
\]
Conclusion
Thus, the correct answer is:
\[
20%
\]