Question

The age of Tarun is one third the age of his mother. If the sum of their age is 48. Find the age of Tarun and his mother?

Answer 1

Hint: In this question, we are given two statements regarding ages of Tarun and his mother. We have to find the actual age of Tarun and his mother. For this, we will first suppose one of their ages as x and then form a linear equation using given statements. After that, we will solve the linear equation to find the ages of Tarun and his mother.

Complete step-by-step answer:
Here, the age of Tarun is one third the age of his mother. Also the sum of their age is 48. Using this information we have to find the actual ages of Tarun and his mother.
Let us suppose that the age of Tarun's mother is x years.
Since Tarun's age is one third the age of his mother, therefore, Tarun's age will be $\dfrac{x}{3}$ years.
Now, we are given a sum of their ages to be 48.
Taking sum of Tarun's age which is $\dfrac{x}{3}$ years with age of Tarun's mother which is x years, we get:
$\dfrac{x}{3}+x=48$.
Now we need to solve this equation to find the value of x which will give us the age of Tarun's mother and then dividing it by three will give us Tarun's age.
Equation formed is $\dfrac{x}{3}+x=48$.
Let us take LCM of 3 on the left side of the equation, we get:
\[\begin{align}
  & \dfrac{x+3x}{3}=48 \\
 & \Rightarrow \dfrac{4x}{3}=48 \\
\end{align}\]
Cross multiplying we get,
\[\begin{align}
  & \Rightarrow 4x=48\times 3 \\
 & \Rightarrow 4x=144 \\
\end{align}\]
Dividing both sides by 4, we get:
\[\Rightarrow \dfrac{4x}{4}=\dfrac{144}{4}\]
Now 4 cancels out on the left side of the equation and we know $144\div 4=36$ so, we are left with x = 36.
Since, x was supposed to be the age of Tarun's mother, therefore, the age of Tarun's mother is 36 years. Age of Tarun is one third the age of his mother, so Tarun's age is $\dfrac{36}{3}=12$ years.

Note: In this question, students can suppose the age of Tarun to be x years, then mother's age will be 3x and sum of ages will be 4x = 48 which will give us x to be equal to 12 years. Students should take care while adding functional value with integer value $\left( x,\dfrac{x}{3} \right)$. Try to solve this equation using one variable only.