Correct Answer - Option 3 : 2 years
Given:
2 years ago, the average age of a family of 7 members was 16 years.
After the inclusion of a newborn baby, the present average age remains the same at 16 years.
Concepts used:
Average age = Sum of ages of all members in the family/Number of members in the family
Calculation:
Let the sum of the present age of all members be x.
So, Two years ago the sum of ages of all the members = x – (2 × 7) = (x – 14) years
The average age of family = (Sum of ages of all the members of the family)/(Number of members in the family)
⇒ 16 years = (x – 14)/7
⇒ x – 14 = 16 × 7
⇒ x – 14 = 112
⇒ x = 112 + 14
⇒ x = 126 years
A new baby is born in the family but the average age of family remains the same at 16 years today.
Let the age of newborn baby be y years.
Sum of ages of all members at present = x + y
⇒ (126 + y) years
Number of members at present in family = 8
The average age of family = 16 = (126 + y)/8
⇒ 16 × 8 = 126 + y
⇒ y = (128 – 126) years
⇒ y = 2 years
∴ The age of new born baby is 2 years.
