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.