Three men rent a farm for Rs. 7000 per annum. A puts 110 cows in the farm for…
2025
Three men rent a farm for Rs. 7000 per annum. A puts 110 cows in the farm for 3 months, B puts 110 cows for 6 months, and C puts 440 cows for 3 months. What percentage of the total expenditure should A pay?
- A.
20%
- B.
14.28%
- C.
16.66%
- D.
11.01%
Attempted by 13 students.
Show answer & explanation
Correct answer: B
Concept
When partners contribute a resource (here, cows) for different durations, their shares of the total expenditure are divided in the ratio of their capital-time products — here, cow-months (cows multiplied by the number of months) — not by the resource amount or the time alone.
Step-by-step working
Compute each partner's cow-months: A = 110 cows × 3 months = 330; B = 110 cows × 6 months = 660; C = 440 cows × 3 months = 1320.
Form the ratio A:B:C = 330:660:1320 and divide throughout by the common factor 330 to simplify: A:B:C = 1:2:4.
Add the parts of the ratio: 1 + 2 + 4 = 7 total parts, so A's share is 1/7 of the total expenditure.
Convert to a percentage: (1/7) × 100 = 14.2857...%, which is given here as 14.28% (truncated to two decimal places, matching how the other percentage options such as 16.66% are also expressed).
Cross-check
Using the total rent of Rs. 7000: A's payment = (1/7) × 7000 = Rs. 1000, B's payment = (2/7) × 7000 = Rs. 2000, and C's payment = (4/7) × 7000 = Rs. 4000; these sum to Rs. 7000, confirming the ratio. Also, (1000/7000) × 100 = 14.28%, matching the value obtained from the ratio method.