## When a person leaves the group and another person joins the group in place of that person then,

Rule 1:
If the average age is increased,
Age of new person = Age of separated person + (Increase in average × total number of persons)

Example

The average age of 10 persons is increased by 5 years when one member of age 40 years is replaced by a new person. What is age of new person?

Sol:

Age of new person = Age of separated person + (Increase in average × total number of persons)

Age of separated person = 40

Increase in average = 5

Total number of persons = 10

Age of new person = 40 + ( 5 × 10 ) = 40 + 50 = 90 years.

Rule 2:

If the average age is decreased,
Age of new person = Age of separated person - (Decrease in average × total number of persons)

Example

Average age of 20 persons is decreased by 1 year when a person aged 25 years is replaced by a new person. What is age of new person?

Sol:

Age of new person = Age of separated person - (Decrease in average × total number of persons)

Age of separated person = 25 years

Decrease in average = 1 year

Age of new person = 25 – (1 × 20) = 25 – 20 = 5 years.

Rule 3:

New average age of group =

Example

A group of 10 persons has an average age of 25 years. A person of that group aged 20 years is replaced by a new person aged 30 years. What is new average of the group?
Sol:

New average age of group =

Provious average = 25 years

Number of persons = 10

Age of leaving person = 20

Age of joining person = 30