Two individuals, A and B rent a pasture. A uses 16 cows for a duration of 3 months and 20 sheep for 4 months, and B uses 30 sheep…

Question

Two individuals, A and B rent a pasture. A uses 16 cows for a duration of 3 months and 20 sheep for 4 months, and B uses 30 sheep for 6 months. If 4 cows are equivalent to 8 sheep, determine A's portion of the rent.

1. A. \(44/89\) (Correct answer)
2. B. \(54/89\)
3. C. \(64/89\)
4. D. \(74/89\)

Correct Answer

Option A — \(44/89\)

Detailed Solution & Explanation

The correct answer is 44/89.

Key Points

• Use the conversion given: 4 cows = 8 sheep, so 1 cow = 2 sheep.
• Express both partners in sheep-months:
  • A: 16 cows × 3 months = 48 cow-months = 48 × 2 = 96; plus 20 sheep × 4 = 80 → 176
  • B: 30 sheep × 6 months = 180
• A's share = 176 / (176 + 180) = 176/356.
• Divide numerator and denominator by 4: 44/89.
• The same template solves every grazing-rent question — convert to one animal, multiply by months, then take the share. Reduce the fraction fully, since the options are given in lowest terms.

Additional Information

• The general template: (units × time) for each partner, summed, then each partner's share is their own total over the combined total.
• Reduce the final fraction fully, since options are always given in lowest terms — 176/356 and 44/89 are the same value but only one will appear.
• Where the conversion is simple (1 cow = 2 sheep), substitute immediately rather than carrying two units through the arithmetic.

प्रश्न (हिन्दी में)

दो व्यक्ति, A और B एक चरागाह किराए पर लेते हैं। A 3 महीने की अवधि के लिए 16 गायों और 4 महीने के लिए 20 भेड़ों का उपयोग करता है और B 6 महीने के लिए 30 भेड़ों का उपयोग करता है। यदि 4 गायें 8 भेड़ों के बराबर हैं, तो किराए में A का हिस्सा निर्धारित करें।

1. A. \(44/89\)
2. B. \(54/89\)
3. C. \(64/89\)
4. D. \(74/89\)