Two individuals, A and B, have rented a field. A places 21 horses in the field for 6 months and 15 cows for 2 months. B adds 15 c…

Question

Two individuals, A and B, have rented a field. A places 21 horses in the field for 6 months and 15 cows for 2 months. B adds 15 cows for 6 months and 40 sheep for 7.5 months. If 3 horses consume the same amount of food as 5 cows, and 6 cows eat as much as 10 sheep, what portion of the rent should A cover?

1. A. \(8/17\) (Correct answer)
2. B. \(19/17\)
3. C. \(16/17\)
4. D. \(20/17\)

Correct Answer

Option A — \(8/17\)

Detailed Solution & Explanation

The correct answer is 8/17.

Key Points

• Convert every animal into one common unit before comparing. Given 3 horses = 5 cows and 6 cows = 10 sheep (so 1 cow = 5/3 sheep):
  • 1 horse = 5/3 cows = 25/9 sheep
• Now compute each partner's sheep-months:
  • A: 21 horses × 6 = 126 horse-months = 126 × 25/9 = 350; plus 15 cows × 2 = 30 cow-months = 30 × 5/3 = 50 → 400
  • B: 15 cows × 6 = 90 cow-months = 90 × 5/3 = 150; plus 40 sheep × 7.5 = 300 → 450
• A's share = 400 / (400 + 450) = 400/850 = 8/17.
• Options B and D exceed 1, which is impossible for a share of rent — a fraction greater than one can be eliminated on sight.

Additional Information

• Grazing-rent questions are partnership questions in disguise: convert every animal to one common unit, multiply by months, and divide the rent in that ratio.
• Chain the conversions carefully when two are given — 3 horses = 5 cows and 6 cows = 10 sheep must be combined to reach horses in sheep.
• A share of a whole must lie between 0 and 1; any option exceeding 1 can be discarded before any calculation, which removes two options here immediately.

प्रश्न (हिन्दी में)

दो व्यक्तियों, A और B ने एक खेत किराए पर लिया है। A 6 महीने के लिए खेत में 21 घोड़े और 2 महीने के लिए 15 गायें रखता है। B 6 महीने के लिए 15 गायें और 7.5 महीने के लिए 40 भेड़ें रखता है। यदि 3 घोड़े 5 गायों के बराबर भोजन खाते हैं, और 6 गायें 10 भेड़ों के बराबर खाती हैं, तो A को किराए का कितना हिस्सा देना चाहिए?

1. A. \(8/17\)
2. B. \(19/17\)
3. C. \(16/17\)
4. D. \(20/17\)