- Step 1: Calculate Total Hills per Hectare:
$$\text{Area} = 10,000\text{ m}^2, \quad \text{Spacing} = 0.20\text{ m} \times 0.20\text{ m} = 0.04\text{ m}^2$$
$$\text{Total Hills} = \frac{10,000}{0.04} = 250,000\text{ hills/ha}$$
- Step 2: Seedlings Required for Planting:
$$\text{Seedlings needed in main field} = 250,000 \times 2 = 500,000\text{ seedlings}$$
- Step 3: Account for 20% Uprooting Damage:
$$\text{Total seedlings required in nursery} = \frac{500,000}{1 - 0.20} = \frac{500,000}{0.80} = 625,000\text{ seedlings}$$
- Step 4: Account for Germination (90%) and Purity (90%):
$$\text{Real Value of Seed} = 0.90 \times 0.90 = 0.81$$
$$\text{Total seeds to be sown} = \frac{625,000}{0.81} \approx 771,605\text{ seeds}$$
- Step 5: Calculate Seed Rate using Test Weight (25 g per 1000 seeds):
$$\text{Seed Rate (kg/ha)} = \frac{771,605 \times 25\text{ g}}{1000 \times 1000} = 19.29\text{ kg/ha} \approx 19.3\text{ kg/ha}$$
- Conclusion: The required seed rate is 19.3 kg/ha. (Correct answer: Option 4)
