The average age was 17 years of a family of 5 members, 3 years ago. A new baby has been born, what is the age of the new baby if the average age of the family is the same baby?

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.

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