Question

Rohit is now one-third of his father's age. After twelve years, the age of Rohit's father will be twice the age of Rohit. Find the present age.

Answer 1

Hint: In this question, we are given a relationship between the present ages of Rohit and his father. Also, we are given relations between their ages after twelve years. We need to find their present ages. For this, we will first suppose the age of Rohit's father’s present age is x years and then find Rohit's age in terms of x using relation. Then we will use a second statement to form an equation in terms of x which will give us a value of x and thus the present ages.

Complete step-by-step solution
Here we are given two statements regarding the relationship between the ages of Rohit and his father. One is for the present age and the other is for age twelve years later. For finding the present ages, let us suppose that the present age of Rohit's father is x years.
Since Rohit's age is one-third of his father's age, so the present age of Rohit becomes $\dfrac{1}{3}x$.
Now, let us find their ages after twelve years.
Age of Rohit's father's after twelve years $\left( x+12 \right)$years.
Age of Rohit after twelve years $\left( \dfrac{x}{3}+12 \right)$years.
Now, we are given that, after twelve years, the age of Rohit's father will be twice the age of Rohit.
Hence, (x+12) is twice of $\left( \dfrac{x}{3}+12 \right)$ which can be represented as:
$x+12=2\left( \dfrac{x}{3}+12 \right)$
Taking LCM of 3 on the right side of the equation, we get:
$\begin{align}
  & \Rightarrow x+12=2\left( \dfrac{x+36}{3} \right) \\
 & \Rightarrow x+12=\dfrac{2x+72}{3} \\
\end{align}$
Cross multiplying we get:
$\begin{align}
  & \Rightarrow 3\left( x+12 \right)=2x+72 \\
 & \Rightarrow 3x+36=2x+72 \\
\end{align}$
Taking variables on one side and constants on the other side we get:
$\begin{align}
  & \Rightarrow 3x-2x=72-36 \\
 & \Rightarrow x=36 \\
\end{align}$
Since, x was supposed to be the age of Rohit's father, so the age of Rohit's father becomes equal to 36.
Now, Rohit's age was ${{\dfrac{1}{3}}^{rd}}$ of his father's age, so age of Rohit becomes equal to $\dfrac{x}{3}=\dfrac{36}{3}=12$.
Hence, the age of Rohit is 12 years and the age of Rohit's father is 36 years.

Note: Students should take care while adding fraction terms with integers. Take care of signs while solving the equation. Students can make the mistake of taking $2\left( x+12 \right)=\left( \dfrac{x}{3}+36 \right)$ which is wrong. We can also solve it using two variables or by taking Rohit's age as x years.