Question

The sum of the ages of $5$ children born at the interval of $3$ years each is $50$ years. What is the age of the youngest child?
$\left( {\text{A}} \right){\text{ }}4$ Years
$\left( {\text{B}} \right){\text{ 8}}$ Years
$\left( {\text{C}} \right){\text{ 10}}$ Years
$\left( {\text{D}} \right)$ None of these

Answer 1

Hint: In this question, we can assume the age of the youngest child is $x$. As it is given that the interval between each child is $3$ years, we assume the age of each child in a series of increasing ages of $3$ years. Then, by adding all the assumed values, equating the total age, and solving it.
Finally we get the required answer.

Complete step-by-step solution:
Let us assume the age of the youngest child is $x$.
Then, the respective assumed ages of the $5$ children born at the interval of $3$ years can be written as $x, x + 3,x + 6,x + 9,x + 12$
It becomes a series of adding $3$ years more than each term in the assumed sequence of ages of the children.
It is given that the sum of the ages of all the $5$ children is equal to $50$ years
So, we can write it as, $x + x + 3 + x + 6 + x + 9 + x + 12 = 50$
By adding the \[x\] terms and constant terms respectively we get,
$ \Rightarrow 5x + 30 = 50$
On subtracting \[30\] on both sides we can write it as,
$ \Rightarrow 5x = 50 - 30$
Let us subtract the RHS we get,
$ \Rightarrow 5x = 20$
On dividing 5 on both sides we get,
,$ \Rightarrow x = 4$
Now, the age of the youngest child is $4$ years.
Hence, the correct option is $\left( {\text{A}} \right)$

Note: In this question, we have to verify the answer:
The age of other children can be found by substituting the obtained value of \[x\] in each of the assumed terms of sequence.
So, we get the ages of all the $5$ children as $4$ years, $7$ years, $10$ years, $13$ years, and $16$ years respectively.
Hence, we can by adding these values which gives us the answer of $50$ years.