Explanation:

We're told that 3 YEARS AGO, the average age of a family of 5 members was 17 years. 
This means that the SUM of their ages was (5)(17) = 85 years.
A baby was born (meaning that there are now 6 family members). We're told that the PRESENT average age of the family members is the SAME.
This means that the sum of the ages is (6)(17) = 102 years.
We're asked for the PRESENT age of the baby.
Since each of the original 5 family members has aged 3 years since the initial average was calculated, the sum of their PRESENT ages is...
85 + (5)(3) = 100.
Since the current sum of the 6 family members is 102, the baby is 102-100 = 2 years old.

Hence, option 1 is the correct answer.