The average age of a group of 8 members is same as it was 3 years ago, when a young member is substituted for an old member, the incoming member is younger to the outgoing member by

Options

A. 11 years
B. 24 years
C. 28 years
D. 16 years

Answer

To solve the problem, we will break it down step by step.

### Step 1: Understand the given information
We know that the average age of a group of 8 members is the same now as it was 3 years ago. This implies that the total age of the group has not changed over the 3 years.

### Step 2: Define the total age 3 years ago
Let’s denote the total age of the 8 members 3 years ago as \( T \).

### Step 3: Calculate the total age now
Since 3 years have passed, each of the 8 members has aged by 3 years. Therefore, the total age of the group now would be:
\[ T + 8 \times 3 = T + 24 \]
However, since the average age remains the same, we conclude that:
\[ T + 24 = T \]
This means that the total age of the group has not changed, which leads us to understand that the increase in age due to time has been offset by the substitution of a younger member for an older member.

### Step 4: Define the ages of the members
Let \( x \) be the age of the outgoing (old) member and \( y \) be the age of the incoming (young) member. According to the problem, the incoming member is younger than the outgoing member by \( d \) years:
\[ y = x - d \]

### Step 5: Set up the equation
When the young member replaces the old member, the total age of the group remains the same:
\[ (T + 24) - x + y = T \]
Substituting \( y \) into the equation gives:
\[ (T + 24) - x + (x - d) = T \]
This simplifies to:
\[ T + 24 - d = T \]

### Step 6: Solve for \( d \)
From the equation \( T + 24 - d = T \), we can isolate \( d \):
\[ 24 - d = 0 \]
Thus, we find:
\[ d = 24 \]

### Conclusion
The incoming member is younger than the outgoing member by 24 years.