Answer :
To solve this problem, let's understand the relationships between the shares of the wife, son, and daughter:
1. Define the shares in terms of the daughter's share:
- Let the daughter's share be \(d\).
- The son's share is twice the daughter's share, so the son's share is \(2d\).
- The wife's share is twice the son's share, so the wife's share is \(2 \times 2d = 4d\).
2. Set up the given condition:
- It's given that the wife's share is ₹9,00,000 more than the daughter's share:
[tex]\[ 4d = d + 900000 \][/tex]
3. Solve the equation:
- Subtract \(d\) from both sides:
[tex]\[ 4d - d = 900000 \][/tex]
[tex]\[ 3d = 900000 \][/tex]
- Divide by 3:
[tex]\[ d = 300000 \][/tex]
So, the daughter's share is ₹300,000.
4. Calculate the son's share:
Since the son's share is twice the daughter's share:
[tex]\[ \text{Son's share} = 2d = 2 \times 300000 = 600000 \][/tex]
5. Calculate the wife's share:
Since the wife's share is twice the son's share:
[tex]\[ \text{Wife's share} = 2 \times 600000 = 1200000 \][/tex]
6. Find the total worth of the property:
Adding up all the shares:
[tex]\[ \text{Total property} = \text{Daughter's share} + \text{Son's share} + \text{Wife's share} \][/tex]
[tex]\[ \text{Total property} = 300000 + 600000 + 1200000 = 2100000 \][/tex]
Therefore, the total worth of the property is ₹21,00,000.
Thus, the correct choice is:
(D) ₹21,00,000
1. Define the shares in terms of the daughter's share:
- Let the daughter's share be \(d\).
- The son's share is twice the daughter's share, so the son's share is \(2d\).
- The wife's share is twice the son's share, so the wife's share is \(2 \times 2d = 4d\).
2. Set up the given condition:
- It's given that the wife's share is ₹9,00,000 more than the daughter's share:
[tex]\[ 4d = d + 900000 \][/tex]
3. Solve the equation:
- Subtract \(d\) from both sides:
[tex]\[ 4d - d = 900000 \][/tex]
[tex]\[ 3d = 900000 \][/tex]
- Divide by 3:
[tex]\[ d = 300000 \][/tex]
So, the daughter's share is ₹300,000.
4. Calculate the son's share:
Since the son's share is twice the daughter's share:
[tex]\[ \text{Son's share} = 2d = 2 \times 300000 = 600000 \][/tex]
5. Calculate the wife's share:
Since the wife's share is twice the son's share:
[tex]\[ \text{Wife's share} = 2 \times 600000 = 1200000 \][/tex]
6. Find the total worth of the property:
Adding up all the shares:
[tex]\[ \text{Total property} = \text{Daughter's share} + \text{Son's share} + \text{Wife's share} \][/tex]
[tex]\[ \text{Total property} = 300000 + 600000 + 1200000 = 2100000 \][/tex]
Therefore, the total worth of the property is ₹21,00,000.
Thus, the correct choice is:
(D) ₹21,00,000
