Average age related problems

Consider, average age of 10 boys is 15. When another boy is included the average age becomes 16. find the new boy's age.

Shortcut formula:

Age of new boy = new avg + (no. of old members x increase in average age).

Hence, age of the boy is = 16 + {10 x (16 - 15) } = 26.

Now if in the above problem the average age decreases by 1 years, when a boy aged 20 is replaced by a new boy. Then,

Age of new boy = age of removed boy - (no. of old members x decrease in average age).

Age of the new boy is =  20 - 10 x 1 = 10.

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Posted in: Age related problems,Average