Question

The average age of a group decreased by 2 years when a person who was 60 years old was replaced by another who was 38 years old. How would the average age change, if this person was replaced by 2 persons who are 49 years old each?

Answer 1

Given:

The average age of a group decreased by 2 years when a person who was 60 years old was replaced by another who was 38 years old.

To find:

The average age change, if this person was replaced by 2 persons who are 49 years old each.

Solution:

1) As per the condition of the question the average decreased by 2 if a person of 60 replaced by person of 38.

Average decreased = Decreased age - increased age

2                                = 60 - 38

2                                = 22

So there are total 11 people in the group

2) Now this person was replaced by 2 persons who are 49 years old each

number of the people = Increased age - decreased age

11                                  =  98 - 60

11                                  =  38

The change in average will be 38/11 years.

The average age change, if this person was replaced by 2 persons who are 49 years old each is $3\frac{5}{11}$ years.