To find the age difference of the new member, we need to compare the average age of the committee before and after the replacement.
Let's assume the average age of the committee members before the replacement is 'x'.
Since the average age remains the same after the replacement, the sum of the ages of the committee members before and after the replacement must be the same.
The total age before the replacement is 10x (since there are 10 members).
After the replacement, the total age will be the sum of the ages of the old members plus the age of the new member.
Since one old member has been replaced by a young member, the sum of the ages of the old members will be 10x - y, where 'y' represents the age difference between the old and new member.
Therefore, the total age after the replacement is (10x - y) + (x - y), which simplifies to 11x - 2y.
Since the total age remains the same, we can equate the expressions for the total age before and after the replacement:
10x = 11x - 2y
Now let's solve for 'y', which represents the age difference between the old and new member:
10x - 11x = -2y
-y = -x
y = x
This means that the age difference between the old and new member is 'x'.
Since we want to find how much younger the new member is, we need to find the value of 'x'.
Since the average age of the committee before the replacement is the same as it was 4 years ago, we can write the equation:
x = x - 4
Simplifying this equation, we get:
4 = 0
This equation has no solution, which means there is a contradiction in the given information. It is not possible for the average age of the committee to remain the same after replacing an old member with a younger member.
Therefore, the question is flawed and does not have a valid solution.