Age related problems- Concept and shortcut formulas

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Condition: When a person joins a group without replacing  any person from group, then

Case 1: Increase in average age
=>Age of new person = previous average age + Number of persons in group (including new person) X increase in average age
                                           OR
=>Age of new person = new average age + Number of persons in group(excluding new person)       X increase in average age

Case 2: Decrease in average age
 Age of new person=  previous average age- number of persons in group ( including new person) X decrease in average age

Example 1: The average age of a class of 20 students is 11 years. If the age of teacher is added  , the average age is increased   by 1 year . What is the age of teacher ?
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Solution: Age of  teacher = new average age + Number of persons in class (including new person) X increase in average age
=(11)+ 21 X 1
So, Age of teacher=32


Condition:  When a person leaves a group without any new person joining

Case 1: Decrease in average age

Age of person left =  previous average age - number of  present persons in group X decrease in the average age

Case 2: Increase in average age

 Age of person left= previous average age + number of present persons in group X increase in average age

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