Question

The average age of a husband and wife five years ago was $25$ years . The average of the present age of husband , wife and a child born during the time of $21$ years . Determine the present age of the child .
A - $1$ years
B - $2$ years
C - $3$ years
D - $4$ years

Answer 1

Hint:
Let us take the present age of Husband is $x$, present age of wife $y$ and the present age of child is $z$ hence from given question The average of the age of a husband and wife five years ago was $25$ years i.e $\dfrac{{x - 5 + y - 5}}{2} = 25$ and the average of the present age of husband , wife and a child born during the time is $21$ years $\dfrac{{x + y + z}}{3} = 21$ solve these two equation get the value of z.

Complete step by step solution:
In this question we have to find out the age of child while the average of the present age of husband , wife and a child born during the time of $21$ years and The average of the age of a husband and wife five years ago was $25$ years
So let us take the present age of Husband is $x$ , present age of wife $y$ and the present age of child is $z$
So from the given question we have to find the value of $z$ .
It is given in the question that the average The average of the age of a husband and wife five years ago was $25$ years
So five years ago the age of wife and husband is $y - 5$ and $x - 5$ respectively ,
Number of person is $2$

Average of number is equal to $ = \dfrac{{{\text{Sum of total age }}}}{{{\text{Total number of person }}}}$
$\Rightarrow \dfrac{{x - 5 + y - 5}}{2} = 25$
On cross multiplication of $5$ we get
$\Rightarrow x + y - 10 = 50$
$\Rightarrow x + y = 60$ ......... equation (i)


It is given in the question that the average of the present age of husband , wife and a child born during the time is $21$ years
Present age of Husband is $x$ , present age of wife $y$ and the present age of child is $z$
Number of person is $2$
Average of number is equal to $ = \dfrac{{{\text{Sum of total age }}}}{{{\text{Total number of person }}}}$
Hence in this = $\dfrac{{x + y + z}}{3} = 21$
On cross multiplication of $3$
$\Rightarrow x + y + z = 63$
we know the value of $x + y = 60$ from above we prove that , on putting this
$\Rightarrow 60 + z = 63$
$\Rightarrow z = 3$

Hence the present age of the child is $3$ years , option C will be correct.

Note:
We can also solve this question without taking any variable x , y , z as we know that Sum of the ages of husband and wife $5$ years ago = $2 \times 25 = 50$ years therefore Sum of the ages of husband and wife at present = $50 + 5 + 5 = 60$ years and Sum of the ages of husband wife and child at present = $3 \times 21$ = $63$ years
Therefore, present age of the child $ = 63 - 60$ years $ = 3$ years
But this method is difficult to understand .