2 years ago the average age of a family of five members was 16 years. A baby having been born the average age of the family is the same today. Find the age of the child .

6 years

 2 years ago , Total age of family of 5 members = 16× 5 = 80 years 

Sum of present age of 5 members = 80 + 5 × 2= 90 years 

but a baby born and average age of present age of 6 members remains same i.e. 16 years 

Sum of present age of 6 members =  16 × 6= 96 years 

Age of baby = 96 - 90 = 6 years