# 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 the same today. The present age of the baby is

A. 3 years

B. 2 years

C. \[{\text{1}}\dfrac{{\text{1}}}{{\text{2}}}\] years

D. 1 years

Answer

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Hint:- Let us find the sum of the ages of 5 members of a family 3 years ago and the sum of the ages of all members of a family (including baby) now. As we know that the average of n number of observations is the sum of all observations divided by the total number of observations (n here).

Complete step-by-step answer -

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

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

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

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

So, now sum of ages of five members of 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 present age of all members of the family including baby will be sum of ages of 5 members + sum of age of 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, average age of family = \[\dfrac{{{\text{Sum of age of all members of family}}}}{{{\text{Total numbers of members in family}}}}\]

So, 17 = \[\dfrac{{{\text{100 + x}}}}{{\text{6}}}\]

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.

Hence the present age of the baby is 2 years.

So, the correct option will be B.

Note:- When we come up with this type of problem then first, we assume the present age of the baby is equal to a variable x. And then we will use the formula of average of n number of observations to get the sum of age of all members of family in both the cases then we will solve that equation to get required value of x.

Complete step-by-step answer -

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

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

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

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

So, now sum of ages of five members of 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 present age of all members of the family including baby will be sum of ages of 5 members + sum of age of 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, average age of family = \[\dfrac{{{\text{Sum of age of all members of family}}}}{{{\text{Total numbers of members in family}}}}\]

So, 17 = \[\dfrac{{{\text{100 + x}}}}{{\text{6}}}\]

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.

Hence the present age of the baby is 2 years.

So, the correct option will be B.

Note:- When we come up with this type of problem then first, we assume the present age of the baby is equal to a variable x. And then we will use the formula of average of n number of observations to get the sum of age of all members of family in both the cases then we will solve that equation to get required value of x.

Last updated date: 20th Sep 2023

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