Six years ago, the average age of 8 family members was 27 years. The present average age of the 3 eldest members is 65 years, and the average age of another 3 members is 20 years. Among the remaining two members, one is 3 years older than the other. What is the age of the elder member among these two?

Question

Accepted Answer

**Solution:**

1. Calculate the total age of all 8 members six years ago:
   - Average age = 27 years
   - Number of members = 8
   - Total age six years ago = $27 	imes 8 = 216$ years

2. Calculate the total present age of all 8 members:
   - Each member has aged 6 years, so total increase = $8 	imes 6 = 48$ years
   - Total present age = $216 + 48 = 264$ years

3. Calculate the total present age of the 3 eldest members:
   - Average age = 65 years
   - Total age = $65 	imes 3 = 195$ years

4. Calculate the total present age of another 3 members:
   - Average age = 20 years
   - Total age = $20 	imes 3 = 60$ years

5. Calculate the total present age of the remaining 2 members:
   - Total age of all 8 members = 264 years
   - Sum of ages of 3 eldest and 3 others = $195 + 60 = 255$ years
   - Therefore, total age of remaining 2 members = $264 - 255 = 9$ years

6. Let the age of the younger member be $x$ years.
   - Then the elder member's age = $x + 3$ years
   - Sum of their ages = $x + (x + 3) = 9$

7. Solve for $x$:
   - $2x + 3 = 9$
   - $2x = 6$
   - $x = 3$

8. Age of elder member = $x + 3 = 3 + 3 = 6$ years

**Answer:** 6 years

Answer

Answer

Answer

Answer