Four milkmen rented a pasture. A grazed 24 cows for 3 months, B grazed 10 cows for 5 months, C grazed 35 cows for 4 months and D grazed 21 cows for 3 months. If A's share of rent is ₹ 720, find the total rent of the field.

Options

A. ₹ 4280
B. ₹ 2240
C. ₹ 3250
D. ₹ 3500

Answer

To solve the problem, we need to calculate the total contribution of each milkman to the pasture based on the number of cows grazed and the duration of grazing. This will help us determine the total rent of the field.

### Step-by-Step Solution:

1. **Calculate the total grazing units for each milkman**:
- For A:
\[ \text{Grazing units} = \text{Number of cows} \times \text{Months} = 24 \text{ cows} \times 3 \text{ months} = 72 \text{ cow-months} \]
- For B:
\[ \text{Grazing units} = 10 \text{ cows} \times 5 \text{ months} = 50 \text{ cow-months} \]
- For C:
\[ \text{Grazing units} = 35 \text{ cows} \times 4 \text{ months} = 140 \text{ cow-months} \]
- For D:
\[ \text{Grazing units} = 21 \text{ cows} \times 3 \text{ months} = 63 \text{ cow-months} \]

2. **Calculate the total grazing units**:
\[ \text{Total grazing units} = 72 + 50 + 140 + 63 = 325 \text{ cow-months} \]

3. **Determine the rent per cow-month**:
- A's share of the rent is ₹720, and A's contribution is 72 cow-months.
- Therefore, the rent per cow-month is calculated as:
\[ \text{Rent per cow-month} = \frac{\text{A's share}}{\text{A's contribution}} = \frac{720}{72} = ₹10 \text{ per cow-month} \]

4. **Calculate the total rent of the field**:
\[ \text{Total rent} = \text{Total grazing units} \times \text{Rent per cow-month} = 325 \times 10 = ₹3250 \]

### Final Answer:
The total rent of the field is ₹3250.

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