Question

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 1

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.