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The average age of the family of five members is 42 years. The oldest family member of the family died and a new member of age 20 years joined them now the average age of family is 36 years. Another family member who was 6 years younger than the oldest member of family left. Find the new average age of the family.

The average age of the family of five members is 42 years. The oldest family member of the family died and a new member of age 20 years joined them now the average age of family is 36 years. Another family member who was 6 years younger than the oldest member of family left. Find the new average age of the family. Correct Answer 34

Given:

Average age of the family of the class = 42

Age of the new member of the family = 20

Total members of the family = 5

Concept Used:

Average = (Sum of value of all the number)/(Total numbers)

Calculations:

Total age of the family = 42 × 5 = 210

Let the oldest person of family be x

∴ Total age of the family = 210 – x

A new member of age 20 joined them

⇒ Total age of the family now = 210 – x +20      ----(I)

It is given the new average of five members of family = 36

⇒ Total age of the family = 36 × 5 = 180      ----(ii)

Equating (i) and (ii)

⇒ 210 – x + 20 = 180

⇒ x = 50

Age of oldest member of the family = 50

Another member 6 years younger than him left the family

∴ Age of the member = 50 – 6 = 44

⇒ Total age of the family = 180 – 44 = 136

∴ Average age of 4 members of family = 136/4 = 34

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