Question

The average age of a group of 8person was 14 years.A person with age 28 years left the group and a new person with age 16 years joined the group.Find the new average age of the group? a)13years. b)14years c)15.5years. d)12.5years​

Answer 1

Answer:

Given that the average age of n number of people is 16 years

Therefore, 16=

n

sum of the ages of n people

⟹sum of the ages of n people=16n -------(1)

Given that the average of the 20 new people is 15 years

Therefore, 15=

20

sum of the ages of 20 new people

⟹sum of the ages of 20 new people=300 -------(2)

Given that after adding 20 new persons the total average becomes 15.5 years

Therefore, 15.5=

20+n

sum of the ages of n people + sum of the ages of the 20 new people

⟹sum of the ages of n people + sum of the ages of the 20 new people=15.5(20+n) -------(3)

substituting (1) and (2) in (3) we get

16n+300=310+15.5n

⟹16n−15.5n=310−300

⟹0.5n=10

⟹n=20

Therefore number of persons initially going for the picnic is 20

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