A sum of Rs.4,27,000 is to be divided among three friends Parbhat, Kuldip and Sandeep such that 3 times Parbhat's share, 4 tunes Kuldip's share and 7 times Sandeep's share are all equal. The share of Sandeep is Rs.:

Options

A. 84000
B. 140000
C. 196000
D. 240000

Answer

To solve the problem of dividing Rs. 4,27,000 among Parbhat, Kuldip, and Sandeep based on the given conditions, we can follow these steps:

### Step 1: Define Variables
Let:
- Parbhat's share = \( P \)
- Kuldip's share = \( K \)
- Sandeep's share = \( S \)

### Step 2: Set Up the Equations
According to the problem:
- \( 3P = 4K = 7S \)

This means that:
- \( P = \frac{4K}{3} \)
- \( K = \frac{7S}{4} \)
- \( P = \frac{7S}{3} \)

### Step 3: Express All Shares in Terms of Sandeep's Share
From the equations:
1. From \( K = \frac{7S}{4} \), we can express \( K \) in terms of \( S \).
2. Substitute \( K \) into the equation for \( P \):
\[ P = \frac{4 \left(\frac{7S}{4}\right)}{3} = \frac{7S}{3} \]

Now we have:
- \( P = \frac{7S}{3} \)
- \( K = \frac{7S}{4} \)
- \( S = S \)

### Step 4: Find a Common Denominator
To combine these shares, we need a common denominator. The least common multiple of 3 and 4 is 12.

Expressing each share in terms of \( S \):
- \( P = \frac{7S}{3} = \frac{28S}{12} \)
- \( K = \frac{7S}{4} = \frac{21S}{12} \)
- \( S = \frac{12S}{12} \)

### Step 5: Write the Total Share Equation
Now, we can write the total amount:
\[ P + K + S = \frac{28S}{12} + \frac{21S}{12} + \frac{12S}{12} = \frac{28S + 21S + 12S}{12} = \frac{61S}{12} \]

### Step 6: Set Up the Total Amount Equation
We know the total amount is Rs. 4,27,000:
\[ \frac{61S}{12} = 4,27,000 \]

### Step 7: Solve for Sandeep's Share
To find \( S \):
\[ 61S = 4,27,000 \times 12 \]
Calculating \( 4,27,000 \times 12 \):
\[ 4,27,000 \times 12 = 51,24,000 \]
Now, divide by 61:
\[ S = \frac{51,24,000}{61} = 84,000 \]

### Conclusion
Sandeep's share is Rs. 84,000.

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