एका गावात 2460 हेक्टर जमीन शेतीखाली आहे. त्यापैकी 57% गव्हाखाली, 52% ज्वारीखाली व 36% गहू आणि ज्वारी व्यतिरीक्त अन्य पिकाखाली आहे, तर गहू आणि ज्वारी ही दोन्ही पिके ज्या जमीनीत काढली जातात अशी किती हेक्टर जमीन गावात आहे ?

The correct answer is Option C (1,107 हेक्टर).

Key Points:
• Set Theory and Venn Diagram Application:
• Total cultivable area = 2460 hectares = 100%.
• Area under other crops outside Wheat and Jowar = 36%.
• Area under Wheat or Jowar or both (n(W ∪ J)):
• n(W ∪ J) = 100% - 36% = 64%
• Given individual crop percentages:
• Wheat (n(W)) = 57%
• Jowar (n(J)) = 52%
• Using the Principle of Inclusion-Exclusion:
• n(W ∪ J) = n(W) + n(J) - n(W ∩ J)
• 64% = 57% + 52% - n(W ∩ J)
• 64% = 109% - n(W ∩ J)
• n(W ∩ J) = 109% - 64% = 45%
• Therefore, 45% of total land grows both crops.
• Total area in hectares:
• Area = 2460 × (45)/(100) = 2460 × 0.45 = 1107 hectares
• Matches Option (3) 1,107 हेक्टर.
• Key Takeaway: Both crops percentage = 57% + 52% - (100% - 36%) = 109% - 64% = 45%; Area = 2460 × 0.45 = 1107 hectares.