Question

# The average age of a family of 6 members 4 years ago was 25 years. Meanwhile a child was born in this family and still the average age of the whole family is the same today. The present age of child is:${\text{A}}{\text{. 2 years}} \\ {\text{B}}{\text{. }}1\dfrac{1}{2}{\text{ years}} \\ {\text{C}}{\text{. 1 year}} \\ {\text{D}}{\text{. Data Insufficient}} \\$

Hint: In this question we have to find the present age of the child using the current average age of the family and the average age of family 4 years ago. So, here we will firstly find the total of their ages using the average which will eventually help us simplify things and reach the answer.

We have been given that the average age of a family of 6 members 4 years ago was 25 years.
So, Sum of the ages of the 6 family members 4 years ago was $25 \times 6 = 150$.
Now, if we know that the sum of ages of the 6 family members 4 years ago was 150, then now in the present the sum of ages of those 6 members will be $= 150 + \left( {4 \times 6} \right) = 150 + 24 = 174$.
Now, in the question we are given that the average age of the family is still 25 in the present. But now in the family there are 7 people because a baby was born.
So, let us consider that the age of the baby is x.
So, the sum of ages of 7 members of the family = 174+ x.
So, using the formula to compute average we get,
$25 = \dfrac{{{\text{Sum of ages of 7 persons}}}}{7} = \dfrac{{174 + {\text{x}}}}{7}$
$\Rightarrow 25 \times 7 = 174 + {\text{x}}$
$\Rightarrow 175 = 174 + {\text{x}}$
$\Rightarrow {\text{x}} = 1$
So, the present age of the child is 1 year.
Hence the correct option is C

Note: Whenever we face such types of problems the crux point to remember is that we need to have a good understanding of how to compute the average of some numbers. Also we should be able to solve linear equations in one variable which helps us in simplification of the problem and reach the correct answer.