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The problem describes a family of four members with specific age-related conditions. Let's break it down:

### Given Information:
1. **Family members:** 'A', 'B', 'C', 'D' (4 members).
2. **Current average age of the family:** 35 years.
   - This means the total current age of the family = \( 35 \times 4 = 140 \) years.
3. **Average age of the eldest and youngest members 6 years from now:** Denoted as 'M'.
4. **Average age of the 3rd youngest and 3rd eldest members 4 years from now:** Denoted as 'N'.
   - We are told \( \frac{M}{N} = \frac{7}{5} \), and 'M' and 'N' are co-prime numbers.
5. **Family structure:**
   - The youngest is 'D', the daughter of 'A' and sister of 'C'.
   - 'B' is female, and the ratio of the present ages of the husband and wife is 7:6.
   - The mother is three times as old as the daughter 'D'.
   - 'A' is the father and the eldest.

### Interpretation of Information:

Let's assign variables for the current ages of each member of the family:

- Let the age of the father ('A') be \( a \),
- Let the age of the mother ('B') be \( b \),
- Let the age of the son ('C') be \( c \),
- Let the age of the daughter ('D') be \( d \) (the youngest).

### Equations Based on the Information:
1. The total age of the family: 
   \[
   a + b + c + d = 140
   \]
2. The mother ('B') is thrice as old as the daughter ('D'): 
   \[
   b = 3d
   \]
3. The ratio of the ages of the husband (A) and wife (B) is 7:6: 
   \[
   \frac{a}{b} = \frac{7}{6} \implies a = \frac{7}{6}b
   \]
4. \( M \) and \( N \) involve the average ages 6 and 4 years from now for specific members, and \( \frac{M}{N} = \frac{7}{5} \).

Given this, we need to solve for the individual ages of all members and then calculate \( M \) and \( N \).

Would you like me to proceed with solving these equations for the ages, or is there a particular part you'd like to focus on?

The present average age of a family of 4 members namely 'A', 'B', 'C' and 'D' is 35 years where the ages of no two persons are the same. Let the average age of the eldest and the youngest members, both taken 6 years hence from now, be 'M' years while the average of the age of the 3rd youngest and 3rd eldest, both taken 4 years ago from now, was 'N', then M:N = 7:5. Neither the mother nor the son are the eldest in the family. The youngest person in the family is 'D', who is the daughter of 'A' and sister of 'C'. The family has one married couple. At present, the mother is thrice as old as the daughter. 'B' is female and the ratio of present ages of husband and wife in the family is 7:6. Also, the father is the eldest.

This problem involves solving a family's age-related word problem using algebra, averages, and ratios. Learn how to determine the ages of four family members based on given conditions, including average age and ratio relationships between parents' and children's ages.

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