Four milkmen rented a pasture. A put to graze 16 cows for 3 months, B 20 cows for 4 months, C 18 cows for 6 months and D 24 cows for 2 months. If A's share of rent be Rs. 2400, the rent paid by C is

Options

A. Rs. 3200
B. Rs. 4200
C. Rs. 4000
D. Rs. 5400

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 they grazed and the time they grazed them.

### Step 1: Calculate the total grazing units for each milkman
The grazing units can be calculated by multiplying the number of cows by the number of months they were grazed.

- **A's contribution**:
\[ 16 \text{ cows} \times 3 \text{ months} = 48 \text{ units} \]

- **B's contribution**:
\[ 20 \text{ cows} \times 4 \text{ months} = 80 \text{ units} \]

- **C's contribution**:
\[ 18 \text{ cows} \times 6 \text{ months} = 108 \text{ units} \]

- **D's contribution**:
\[ 24 \text{ cows} \times 2 \text{ months} = 48 \text{ units} \]

### Step 2: Write the total contribution in ratio form
Now we can express the contributions as a ratio:
\[ A : B : C : D = 48 : 80 : 108 : 48 \]

### Step 3: Simplify the ratio
To simplify the ratio, we can divide each term by 4:
\[ A : B : C : D = 12 : 20 : 27 : 12 \]

### Step 4: Calculate the total parts of the ratio
Now, we sum up the parts of the ratio:
\[ 12 + 20 + 27 + 12 = 71 \text{ parts} \]

### Step 5: Determine the value of one part
We know that A's share is Rs. 2400, which corresponds to 12 parts:
\[ \text{Value of one part} = \frac{2400}{12} = 200 \text{ Rs.} \]

### Step 6: Calculate C's share
C's share corresponds to 27 parts:
\[ \text{C's share} = 27 \times 200 = 5400 \text{ Rs.} \]

### Final Answer
Thus, the rent paid by C is Rs. 5400.

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