Four milkmen rented a pasture . A grazed 18 cows for 4 montsh, B grazed 25 cows for 2 montsh, C grazed 28 cows for 5 months and D grazed 21 cows for 3 montsh. If A's share of rent is X 720, what will be the total rent of the pasture ?

Options

A. X 1650
B. X 3250
C. X 35000
D. X 3000

Answer

To solve the problem step by step, we will calculate the contribution of each milkman to the rent based on the number of cows grazed and the duration for which they were grazed.

### Step 1: Calculate the contribution of each milkman
We need to find the total contribution of each milkman in terms of "cow-months," which is calculated as the number of cows multiplied by the number of months they were grazed.

- **A's contribution**:
\[ 18 \text{ cows} \times 4 \text{ months} = 72 \text{ cow-months} \]

- **B's contribution**:
\[ 25 \text{ cows} \times 2 \text{ months} = 50 \text{ cow-months} \]

- **C's contribution**:
\[ 28 \text{ cows} \times 5 \text{ months} = 140 \text{ cow-months} \]

- **D's contribution**:
\[ 21 \text{ cows} \times 3 \text{ months} = 63 \text{ cow-months} \]

### Step 2: Calculate the total contribution
Now, we will add up all the contributions to find the total number of cow-months.

\[ \text{Total cow-months} = 72 + 50 + 140 + 63 = 325 \text{ cow-months} \]

### Step 3: Determine the value of one unit
We know that A's share of the rent is ₹720, which corresponds to A's contribution of 72 cow-months. Therefore, we can find the value of one cow-month.

\[ \text{Value of one unit} = \frac{720}{72} = 10 \text{ rupees per cow-month} \]

### Step 4: Calculate the total rent
To find the total rent of the pasture, we multiply the total number of cow-months by the value of one cow-month.

\[ \text{Total rent} = 325 \text{ cow-months} \times 10 \text{ rupees/cow-month} = 3250 \text{ rupees} \]

### Final Answer
The total rent of the pasture is **₹3250**.

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