A sum off Rs 4680 was divided among Parthu, Kunti and Arjun in the ratio of `(1)/(2):(1)/(3):(1)/(4)` find the sahre of Parthu. (in Rs)

Options

A. 1440
B. 1080
C. 2160
D. none of these

Explanation

To solve the problem of dividing Rs 4680 among Parthu, Kunti, and Arjun in the ratio of \( \frac{1}{2} : \frac{1}{3} : \frac{1}{4} \), we can follow these steps:

### Step 1: Write the Ratios
The given ratio is \( \frac{1}{2} : \frac{1}{3} : \frac{1}{4} \).

### Step 2: Find the LCM of the Denominators
To simplify the ratios, we need to find the least common multiple (LCM) of the denominators (2, 3, and 4).

The LCM of 2, 3, and 4 is 12.

### Step 3: Convert the Ratios
Now, we will convert each fraction to have a common denominator of 12:
- For \( \frac{1}{2} \):
\[ \frac{1}{2} = \frac{1 \times 6}{2 \times 6} = \frac{6}{12} \]
- For \( \frac{1}{3} \):
\[ \frac{1}{3} = \frac{1 \times 4}{3 \times 4} = \frac{4}{12} \]
- For \( \frac{1}{4} \):
\[ \frac{1}{4} = \frac{1 \times 3}{4 \times 3} = \frac{3}{12} \]

Thus, the ratio becomes \( 6 : 4 : 3 \).

### Step 4: Assign Variables
Let the common factor be \( K \). Therefore, we can express the shares as:
- Parthu's share = \( 6K \)
- Kunti's share = \( 4K \)
- Arjun's share = \( 3K \)

### Step 5: Set Up the Equation
The total amount shared among them is Rs 4680. Therefore, we can write the equation:
\[ 6K + 4K + 3K = 4680 \]
This simplifies to:
\[ 13K = 4680 \]

### Step 6: Solve for K
Now, we can solve for \( K \):
\[ K = \frac{4680}{13} = 360 \]

### Step 7: Find Parthu's Share
Now that we have \( K \), we can find Parthu's share:
\[ \text{Parthu's share} = 6K = 6 \times 360 = 2160 \]

### Final Answer
Thus, Parthu's share is Rs 2160.

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