Four milkmen rented a pasture.A grazed 18 cows for 4 months, B, 25 cows for 2 months. C, 28 cows for 5 months and D, 21 cows for 3 months. If A's share of rent is Rs. 360, the total rent of the field is

Options

A. Rs 1500
B. Rs 1600
C. Rs 1625
D. Rs 1620

Answer

To solve the problem step by step, we need to determine the total rent of the pasture based on the contributions of each milkman. Here’s how we can do it:

### Step 1: Calculate the total grazing months for each milkman
- **A** grazed 18 cows for 4 months:
\[ \text{A's contribution} = 18 \text{ cows} \times 4 \text{ months} = 72 \text{ cow-months} \]
- **B** grazed 25 cows for 2 months:
\[ \text{B's contribution} = 25 \text{ cows} \times 2 \text{ months} = 50 \text{ cow-months} \]
- **C** grazed 28 cows for 5 months:
\[ \text{C's contribution} = 28 \text{ cows} \times 5 \text{ months} = 140 \text{ cow-months} \]
- **D** grazed 21 cows for 3 months:
\[ \text{D's contribution} = 21 \text{ cows} \times 3 \text{ months} = 63 \text{ cow-months} \]

### Step 2: Find the total cow-months
Now, we add up all the contributions:
\[ \text{Total cow-months} = 72 + 50 + 140 + 63 = 325 \text{ cow-months} \]

### Step 3: Determine the ratio of contributions
The contributions can be expressed as a ratio:
\[ \text{Ratio of A : B : C : D} = 72 : 50 : 140 : 63 \]
To simplify this ratio, we can divide each term by their greatest common divisor (GCD), but for our purpose, we will keep the values as they are.

### Step 4: Calculate A's share of the total rent
We know A's share of the rent is Rs. 360. Since A's contribution is 72 cow-months out of a total of 325 cow-months, we can set up the equation:
\[ \frac{A's \text{ share}}{\text{Total rent}} = \frac{72}{325} \]
Let the total rent be \( x \):
\[ \frac{360}{x} = \frac{72}{325} \]

### Step 5: Solve for the total rent \( x \)
Cross-multiplying gives us:
\[ 360 \times 325 = 72 \times x \]
Calculating \( 360 \times 325 \):
\[ 360 \times 325 = 117000 \]
Now, we can solve for \( x \):
\[ 72x = 117000 \implies x = \frac{117000}{72} \]
Calculating \( \frac{117000}{72} \):
\[ x = 1625 \]

### Conclusion
The total rent of the pasture is Rs. 1625.