A, B and C rent a pasture. A puts in 10 oxen for 7 months, B 12 oxen for 5 months and C 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?

Options

A. Rs. 45/-
B. Rs. 50/-
C. Rs.55/-
D. Rs. 60/-

Answer

To solve the problem, we need to determine how much each person contributed to the total grazing effort in terms of "oxen-months" and then calculate C's share of the rent based on that contribution.

### Step-by-Step Solution:

1. **Calculate the total oxen-months contributed by each person:**
- A contributed:
\[ 10 \text{ oxen} \times 7 \text{ months} = 70 \text{ oxen-months} \]
- B contributed:
\[ 12 \text{ oxen} \times 5 \text{ months} = 60 \text{ oxen-months} \]
- C contributed:
\[ 15 \text{ oxen} \times 3 \text{ months} = 45 \text{ oxen-months} \]

2. **Calculate the total oxen-months contributed by all three:**
\[ \text{Total oxen-months} = 70 + 60 + 45 = 175 \text{ oxen-months} \]

3. **Determine the share of rent per oxen-month:**
\[ \text{Rent per oxen-month} = \frac{\text{Total Rent}}{\text{Total oxen-months}} = \frac{175 \text{ Rs}}{175 \text{ oxen-months}} = 1 \text{ Rs per oxen-month} \]

4. **Calculate C's share of the rent:**
- Since C contributed 45 oxen-months, C's share of the rent is:
\[ \text{C's share} = 45 \text{ oxen-months} \times 1 \text{ Rs per oxen-month} = 45 \text{ Rs} \]

### Final Answer:
C must pay Rs. 45 as his share of the rent.