What is the average age of the six members A, B, C, D, E and F in the family?
I. Average age of D and E is 30 yr
II. Average are of A,B,C and F is 50 yr
III. Average of A,B,D and E is 40 yr

Options

A. I and II
B. I and III
C. II and III
D. any two three

Answer

To find the average age of the six members A, B, C, D, E, and F in the family, we need to analyze the information provided in the statements.

### Step-by-Step Solution:

1. **Understanding the Average Formula**:
The average age of the six members can be calculated using the formula:
\[ \text{Average} = \frac{A + B + C + D + E + F}{6} \]
Therefore, to find the average, we need the total sum of their ages \(A + B + C + D + E + F\).

2. **Analyzing Statement I**:
- Statement I states that the average age of D and E is 30 years.
- This implies:
\[ \frac{D + E}{2} = 30 \implies D + E = 60 \]

3. **Analyzing Statement II**:
- Statement II states that the average age of A, B, C, and F is 50 years.
- This implies:
\[ \frac{A + B + C + F}{4} = 50 \implies A + B + C + F = 200 \]

4. **Analyzing Statement III**:
- Statement III states that the average age of A, B, D, and E is 40 years.
- This implies:
\[ \frac{A + B + D + E}{4} = 40 \implies A + B + D + E = 160 \]

5. **Combining Statements**:
- From Statement I, we have \(D + E = 60\).
- From Statement III, we can substitute \(D + E\) into the equation:
\[ A + B + 60 = 160 \implies A + B = 100 \]

6. **Finding Total Age**:
- Now we can substitute \(A + B\) into Statement II:
\[ A + B + C + F = 200 \implies 100 + C + F = 200 \implies C + F = 100 \]

7. **Total Age of All Members**:
- Now we can find the total age of all six members:
\[ A + B + C + D + E + F = (A + B) + (C + F) + (D + E) = 100 + 100 + 60 = 260 \]

8. **Calculating the Average**:
- Finally, we can calculate the average age:
\[ \text{Average} = \frac{A + B + C + D + E + F}{6} = \frac{260}{6} \approx 43.33 \]

### Conclusion:
The average age of the six members A, B, C, D, E, and F is approximately 43.33 years.