A farmer owns 12 ha of land. He follows a crop rotation plan where 40 % of the land is sown with maize, 35 % with soybean, and the rest with rice. Calculate (a) the area sown with soybean and (b) the total expected yield if the yields per hectare are: maize = 6 t /ha, soybean = 2 t /ha, rice = 4 t /ha.
Answer
Soybean area = 4.2 ha; Total yield = 49.2 t
The correct answer is Soybean area = 4.2 ha; Total yield = 49.2 t — Step 8: State the results – soybean area is 4.2 ha and total expected yield is 49.2 t.
Step-by-step solution
- Step 1: Compute area under soybean: 35% of 12 ha → 0.35 × 12 = 4.2 ha.
- Step 2: Compute area under maize: 40% of 12 ha → 0.40 × 12 = 4.8 ha.
- Step 3: Compute area under rice: remaining area = 12 ha − 4.8 ha − 4.2 ha = 3 ha.
- Step 4: Calculate yield for maize: 4.8 ha × 6 t ha⁻¹ = 28.8 t.
- Step 5: Calculate yield for soybean: 4.2 ha × 2 t ha⁻¹ = 8.4 t.
- Step 6: Calculate yield for rice: 3 ha × 4 t ha⁻¹ = 12 t.
- Step 7: Sum the yields: 28.8 t + 8.4 t + 12 t = 49.2 t.
- Step 8: State the results – soybean area is 4.2 ha and total expected yield is 49.2 t.
Common mistake: Mixing up percentages or not computing the remaining area for rice
Concept tested: Crop rotation area & yield calculation
Published · How this solution was prepared and checked
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