3 years ago, the average age of a family of 5 members was 17 years. A baby having been born, the average age of the family is same today. The present age of the baby is

As we know , average = $$\frac{Sum}{Number of elements}$$

so 3 years ago total sum of all 5 members = 17 x 5 = 85

so after 3 years, every person will be 3 years older and hence total increase in sum of ages will be 15 years and hence present total age = 85 + 15 = 100 years

let the present age of baby be z years so ,

total age of all 6 members = 100+z

it is given that new average of 6 members is same as 0f 5 years 3 years ago i.e. 17 years ,So,

17 = $$\frac{100+z}{6}$$

z= 2 years