1. **State the problem:** We need to calculate the efficiency of a Carnot engine operating between a hot reservoir at temperature $T_h=500$ K and a cold reservoir at temperature $T_c=300$ K. 2. **Formula for Carnot efficiency:** The efficiency $\eta$ of a Carnot engine is given by $$\eta = 1 - \frac{T_c}{T_h}$$ where $T_c$ and $T_h$ are the absolute temperatures of the cold and hot reservoirs respectively. 3. **Calculate the efficiency:** Substitute the given values: $$\eta = 1 - \frac{300}{500} = 1 - 0.6 = 0.4$$ 4. **Convert to percentage:** $$\eta = 0.4 \times 100 = 40\%$$ 5. **Interpretation:** The efficiency of the Carnot engine is 40%, which corresponds to option (i).