In the family of Amit, there are 4 members- Amit, his wife, his only son and his only daughter. Three years ago, age of Amit was 4 years more than the sum of the ages of his son and daughter, then what is the present age of their daughter?
I. Amit's wife is 7 years younger to him and her present age is twice the present age of their son.
II. Three years hence, the respective ratio between the ages of his daughter and his son will be 6 : 5.
III. Two years hence, the age of Amit will be 1 years less than the sum of the ages of his son and daughter.
Which of the following statement(s) is/are sufficient to answer the question?

Options

A. All the three statements together
B. Only statement III
C. Only statements II and III together
D. Only statements I and III together

Explanation

To solve the problem, we will define the variables for the ages of the family members and use the information provided in the statements to derive equations.

### Step 1: Define Variables
Let:
- Amit's present age = A
- Amit's wife's present age = W
- Amit's son's present age = S
- Amit's daughter's present age = D

### Step 2: Set Up the Equations
From the information given:
1. **From Statement I**:
- Amit's wife is 7 years younger than him:
\[ W = A - 7 \]
- His wife's present age is twice the present age of their son:
\[ W = 2S \]

2. **From Statement II**:
- Three years hence, the ratio of the ages of his daughter and son will be 6:5:
\[ \frac{D + 3}{S + 3} = \frac{6}{5} \]
- Cross-multiplying gives:
\[ 5(D + 3) = 6(S + 3) \]
\[ 5D + 15 = 6S + 18 \]
\[ 5D = 6S + 3 \]
\[ D = \frac{6S + 3}{5} \]

3. **From Statement III**:
- Two years hence, Amit's age will be 1 year less than the sum of the ages of his son and daughter:
\[ A + 2 = (S + 2) + (D + 2) - 1 \]
\[ A + 2 = S + D + 3 \]
\[ A = S + D + 1 \]

### Step 3: Substitute and Solve
Now we have three equations:
1. \( W = A - 7 \)
2. \( W = 2S \)
3. \( A = S + D + 1 \)

Substituting \( W = 2S \) into \( W = A - 7 \):
\[ 2S = A - 7 \]
\[ A = 2S + 7 \]

Now substitute \( A = 2S + 7 \) into \( A = S + D + 1 \):
\[ 2S + 7 = S + D + 1 \]
\[ 2S + 7 - S - 1 = D \]
\[ D = S + 6 \]

### Step 4: Find the Present Age of Daughter
Now we have \( D = S + 6 \). To find the present age of the daughter, we need the value of \( S \).

Using the equation \( D = \frac{6S + 3}{5} \) from Statement II:
Substituting \( D = S + 6 \):
\[ S + 6 = \frac{6S + 3}{5} \]

Cross-multiplying gives:
\[ 5(S + 6) = 6S + 3 \]
\[ 5S + 30 = 6S + 3 \]
\[ 30 - 3 = 6S - 5S \]
\[ 27 = S \]

Now substituting \( S = 27 \) back into \( D = S + 6 \):
\[ D = 27 + 6 = 33 \]

### Conclusion
The present age of Amit's daughter is **33 years**.