Each of the following question is followed by two statements I, and Il. You have to study the question and the statements and decide which of the statement(s) is/are necessary to answer the question.
What is the average age of family?
Statement I: The age of Father is twice age of son who is 4 years elder to his sister whose age is half of her mother,
Statement II: The age of oldest person is 40 years and there are only 4 persons in the family.

Options

A. Only Statement I alone.
B. Only Statement II alone.
C. Both Statements I and II together.
D. Neither Statement I nor II is sufficient

Answer

To determine the average age of the family, we need to analyze the information provided in both statements.

### Step-by-Step Solution:

1. **Understanding the Question**:
We need to find the average age of the family.

2. **Analyzing Statement I**:
- The statement provides relationships between the ages of the family members:
- Let the age of the son be \( S \).
- The father’s age is twice the age of the son: \( F = 2S \).
- The son is 4 years older than his sister: \( S = S_{sister} + 4 \) (where \( S_{sister} \) is the sister's age).
- The sister’s age is half of the mother’s age: \( S_{sister} = \frac{M}{2} \) (where \( M \) is the mother's age).
- From this, we can express all ages in terms of one variable, say the sister's age \( S_{sister} \):
- \( S_{sister} = S_{sister} \)
- \( S = S_{sister} + 4 \)
- \( F = 2(S_{sister} + 4) \)
- \( M = 2S_{sister} \)

3. **Analyzing Statement II**:
- The statement tells us that the oldest person is 40 years old and there are 4 members in the family.
- Since the father is likely the oldest person, we can set \( F = 40 \).

4. **Combining the Statements**:
- From Statement II, we have \( F = 40 \).
- Using Statement I, we can set up the equation:
\[ 2(S_{sister} + 4) = 40 \]
- Solving for \( S_{sister} \):
\[ S_{sister} + 4 = 20 \implies S_{sister} = 16 \]
- Now we can find the ages:
- Sister's age \( S_{sister} = 16 \)
- Son's age \( S = S_{sister} + 4 = 16 + 4 = 20 \)
- Mother's age \( M = 2S_{sister} = 2 \times 16 = 32 \)
- Father's age \( F = 40 \)

5. **Calculating the Average Age**:
- Now we have all ages:
- Father: 40 years
- Mother: 32 years
- Son: 20 years
- Sister: 16 years
- The average age is calculated as follows:
\[ \text{Average Age} = \frac{F + M + S + S_{sister}}{4} = \frac{40 + 32 + 20 + 16}{4} = \frac{108}{4} = 27 \]

### Conclusion:
The average age of the family is **27 years**.