A man divided his property so that his son's share to his wife's and wife's share to his wife's and wife's share to his daughter's are both as in the ratio 3: 1. If the daughters get Rs 10,000 less than son, the value (in rupees) of the whole property is :

Options

A. Rs 16,250
B. Rs 16,000
C. Rs 18,200
D. Rs 17,000

Answer

To solve the problem step-by-step, we will follow these steps:

### Step 1: Understand the Ratios
The problem states that the ratio of the son's share to the wife's share is 3:1, and the ratio of the wife's share to the daughter's share is also 3:1.

Let:
- Son's share = 3x
- Wife's share = 1x
- Daughter's share = 1y

Since the wife's share is the same in both ratios, we can equate the two ratios.

### Step 2: Set Up the Equations
From the ratios, we have:
- Son's share = 3x
- Wife's share = 1x
- Daughter's share = (1/3) * Wife's share = (1/3) * 1x = (1/3)x

### Step 3: Relate the Shares
According to the problem, the daughters get Rs 10,000 less than the son. Therefore, we can set up the equation:
\[ 3x - \frac{1}{3}x = 10,000 \]

### Step 4: Solve for x
To solve the equation, first, we need to express everything with a common denominator:
\[ 3x - \frac{1}{3}x = 10,000 \]
Convert \(3x\) to a fraction:
\[ \frac{9}{3}x - \frac{1}{3}x = 10,000 \]
Combine the fractions:
\[ \frac{9x - 1x}{3} = 10,000 \]
This simplifies to:
\[ \frac{8x}{3} = 10,000 \]
Now, multiply both sides by 3:
\[ 8x = 30,000 \]
Now, divide by 8:
\[ x = \frac{30,000}{8} = 3,750 \]

### Step 5: Calculate the Shares
Now that we have the value of \(x\), we can calculate the shares:
- Son's share = \(3x = 3 \times 3,750 = 11,250\)
- Wife's share = \(1x = 3,750\)
- Daughter's share = \(\frac{1}{3}x = \frac{1}{3} \times 3,750 = 1,250\)

### Step 6: Calculate the Total Property Value
Now, we need to find the total property value. The total property is the sum of all shares:
\[ \text{Total Property} = \text{Son's share} + \text{Wife's share} + \text{Daughter's share} \]
\[ = 11,250 + 3,750 + 1,250 \]
\[ = 16,250 \]

### Final Answer
The value of the whole property is **Rs 16,250**.

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