Explanation

So, now we know that the average age of 5 members of a family 3 years ago is 17 years.

So, the sum of the ages of all members of the family 3 years ago will be (average age)*5.

The sum of the ages of the five members of the family 3 years ago will be 17*5 = 85 years.

As we know, now the age of all 5 members of the family should be 3 more than the age they had 3 years ago.

So, now the sum of the ages of the five members of the family should be 85 + 3*5 = 100.

But as we know that in three years a baby has also been born in the family.

Let the baby be born x years ago.

So, the current age of the baby will be x years.

So, now the sum of the present age of all members of the family including the baby will be the sum of the ages of 5 members + the sum of the ages of the baby.

So, today the sum of the ages of all 6 members of the family will be (100 + x) years.

Now as we are given that today the average age of the family is also 17 years.

So, the average age of the family is = Sum of the age of all members of the family / total number of members in a family

So, 17 = 100 + x6

Now, cross-multiplying the above equation to get the value of x.

17*6 = 100 + x

102 = 100 + x

So, x = 102 – 100 = 2 years.