A, B, C rent a pasture. A puts 10 oxen for 7 months, B puts 12 oxen for 5…
2024
A, B, C rent a pasture. A puts 10 oxen for 7 months, B puts 12 oxen for 5 months and C puts 15 oxen for 3 months for grazing. If the rent of the pasture is Rs. 175, how much must C pay as his share of rent?
- A.
Rs. 45
- B.
Rs. 50
- C.
Rs. 55
- D.
Rs. 60
Show answer & explanation
Correct answer: A
In a partnership where partners contribute resources for different time periods, each partner's share of the total profit or rent is divided in the ratio of the product of the quantity contributed and the time period for which it was contributed (quantity x time) -- not by quantity alone or time alone.
Find the contribution (oxen x months) for each partner: A = 10 oxen x 7 months = 70 units.
B = 12 oxen x 5 months = 60 units.
C = 15 oxen x 3 months = 45 units.
Write the ratio of the three contributions: A : B : C = 70 : 60 : 45, which reduces to 14 : 12 : 9 (dividing every term by 5).
Total parts = 14 + 12 + 9 = 35.
C's share of the rent = (9/35) x Rs. 175 = Rs. 45.
Check: A's share = (14/35) x 175 = Rs. 70, and B's share = (12/35) x 175 = Rs. 60. Adding all three shares gives Rs. 70 + Rs. 60 + Rs. 45 = Rs. 175, which equals the total rent, confirming the split is correct.