A man divided his property so that his son's share to his wife's and wife's share to his daughter's are both as in the ratio 5:2. If the daughter gets Rs 29,400 less than son the value (in rupees) of the whole property is

Options

A. Rs 54600
B. Rs 56,000
C. Rs 52650
D. Rs 58500

Answer

To solve the problem, we need to determine the total value of the man's property based on the ratios given and the information about the daughter's share.

### Step-by-Step Solution:

1. **Understanding the Ratios**:
- The ratio of the son's share to the wife's share is given as 5:2.
- The ratio of the wife's share to the daughter's share is also given as 5:2.

2. **Setting Up the Variables**:
- Let the son's share be \( 5x \).
- Let the wife's share be \( 2x \).
- Since the wife's share is common in both ratios, we can express the daughter's share in terms of the wife's share:
- If the wife's share is \( 2x \), then the daughter's share (using the same ratio) will be \( \frac{2}{5} \times 2x = \frac{4x}{5} \).

3. **Finding the Difference**:
- According to the problem, the daughter receives Rs 29,400 less than the son.
- Therefore, we can set up the equation:
\[ 5x - \frac{4x}{5} = 29,400 \]

4. **Solving the Equation**:
- To solve the equation, first convert \( 5x \) into a fraction with a common denominator:
\[ 5x = \frac{25x}{5} \]
- Now, substitute this back into the equation:
\[ \frac{25x}{5} - \frac{4x}{5} = 29,400 \]
- Combine the fractions:
\[ \frac{25x - 4x}{5} = 29,400 \]
\[ \frac{21x}{5} = 29,400 \]

5. **Isolating x**:
- Multiply both sides by 5 to eliminate the denominator:
\[ 21x = 29,400 \times 5 \]
\[ 21x = 147,000 \]
- Now, divide both sides by 21:
\[ x = \frac{147,000}{21} = 7,000 \]

6. **Calculating Individual Shares**:
- Now that we have \( x \), we can find the shares:
- Son's share: \( 5x = 5 \times 7,000 = 35,000 \)
- Wife's share: \( 2x = 2 \times 7,000 = 14,000 \)
- Daughter's share: \( \frac{4x}{5} = \frac{4 \times 7,000}{5} = 5,600 \)

7. **Calculating Total Property Value**:
- The total property value is the sum of the shares:
\[ \text{Total Property} = \text{Son's share} + \text{Wife's share} + \text{Daughter's share} \]
\[ \text{Total Property} = 35,000 + 14,000 + 5,600 = 54,600 \]

### Final Answer:
The value of the whole property is **Rs 54,600**.