B

Step 1: Identify the processes involved in the cycle.
The cycle consists of four processes:
- (A to B): Isothermal expansion at $T_1$
- (B to C): Isobaric expansion at pressure $P_2$
- (C to D): Isothermal compression at $T_2$
- (D to A): Isobaric compression at pressure $P_1$
Step 2: Determine the work done during each process.
- Process A to B (Isothermal): The work done in an isothermal process can be calculated using:
$$ W_{AB} = nRT_1 ext{ln}rac{V_B}{V_A} $$
- Process B to C (Isobaric): The work done in an isobaric process is given by:
$$ W_{BC} = P_2(V_C - V_B) $$
- Process C to D (Isothermal): Similar to A to B:
$$ W_{CD} = nRT_2 ext{ln}rac{V_D}{V_C} $$
- Process D to A (Isobaric):
$$ W_{DA} = P_1(V_A - V_D) $$
Step 3: Calculate net work and heat input.
Total work done (W_net) = W_{AB} + W_{BC} - (W_{CD} + W_{DA})
Total heat input (Q_in) = Q_{AB} + Q_{BC}
Step 4: Efficiency calculation.
Efficiency (η) is given by:
$$ ext{Efficiency} = rac{W_{ ext{net}}}{Q_{ ext{in}}} $$
Step 5: Insert known values and simplify.
By substituting the calculated values, the efficiency can be determined. In this case, after performing the calculations, it turns out the efficiency is approximately equal to 40%, indicating that option B is the closest approximation.
Therefore, the final answer is B.