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}} \\
$
Answer
363.3k+ views
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.
Complete step-by-step 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.
Complete step-by-step 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.
Last updated date: 28th Sep 2023
•
Total views: 363.3k
•
Views today: 7.63k
Recently Updated Pages
What do you mean by public facilities

Slogan on Noise Pollution

Paragraph on Friendship

Disadvantages of Advertising

Prepare a Pocket Guide on First Aid for your School

What is the Full Form of ILO, UNICEF and UNESCO

Trending doubts
How do you solve x2 11x + 28 0 using the quadratic class 10 maths CBSE

Summary of the poem Where the Mind is Without Fear class 8 english CBSE

The poet says Beauty is heard in Can you hear beauty class 6 english CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Difference Between Plant Cell and Animal Cell

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

What is the past tense of read class 10 english CBSE

The equation xxx + 2 is satisfied when x is equal to class 10 maths CBSE

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE
