Six years ago, average age of 8 family members was 27 years. Present average of 3 eldest members is 65 years and another 3 member's average age is 20 years. Out of remaining two one is 3 years elder. Find age of elder member out of remaining two?

Options

A. A)6 years
B. B)5 years
C. C)4 years
D. D)7 years

Answer

To solve the problem step by step, we will break down the information given and use it to find the age of the elder member out of the remaining two.

### Step 1: Calculate the current average age of the family members
The average age of the 8 family members six years ago was 27 years. To find the current average age, we add 6 years to the average age from six years ago.

\[ \text{Current Average Age} = 27 + 6 = 33 \text{ years} \]

### Step 2: Calculate the total current age of the family members
To find the total current age of all 8 family members, we multiply the current average age by the number of members.

\[ \text{Total Current Age} = 33 \times 8 = 264 \text{ years} \]

### Step 3: Calculate the total age of the three eldest members
The average age of the three eldest members is given as 65 years. Therefore, we can calculate their total age.

\[ \text{Total Age of Eldest Members} = 65 \times 3 = 195 \text{ years} \]

### Step 4: Calculate the total age of the next three members
The average age of the next three members is given as 20 years. We can calculate their total age as well.

\[ \text{Total Age of Next Members} = 20 \times 3 = 60 \text{ years} \]

### Step 5: Calculate the total age of the remaining two members
We have the total current age of all members (264 years) and we can find the total age of the remaining two members by subtracting the total ages of the three eldest and the next three members from the total age.

\[ \text{Total Age of Remaining Two Members} = 264 - (195 + 60) = 264 - 255 = 9 \text{ years} \]

### Step 6: Set up equations for the remaining two members
Let the age of the younger member be \( H \) and the elder member be \( G \). We know that:

1. \( G + H = 9 \) (from the total age of the remaining two members)
2. \( G = H + 3 \) (since one is 3 years elder)

### Step 7: Solve the equations
Substituting the second equation into the first:

\[ (H + 3) + H = 9 \]
\[ 2H + 3 = 9 \]
\[ 2H = 9 - 3 \]
\[ 2H = 6 \]
\[ H = 3 \]

Now substituting \( H \) back to find \( G \):

\[ G = H + 3 = 3 + 3 = 6 \]

### Conclusion
The age of the elder member out of the remaining two is \( G = 6 \) years.