Question

Two years ago, Mohit was three times as old as his son and two years hence, twice of Mohit’s age will be equal to five times that of his son. Then the present age of Mohit is
A. $14$ years
B. $38$ years
C. $32$ years
D. $34$ years

Answer 1

Hint: To begin this question, we have to define a term that is the reference for all ages in this question. Since in the very beginning, Mohit’s age has been defined with respect to his son’s age, hence we can conclude that the basic reference point has to be Mohit’s son. So now, we can assume Mohit’s son’s present age to be $x$ years and define all other ages with respect to his son’s present age.

Complete step-by-step answer:
In the very beginning, we have defined Mohit’s son’s present age as $x$ years. We can take Mohit’s present age to be $y$ years.
The first timeline we have is from two years ago. Using normal annual calculations, Mohit’s son’s age at that time would be $x - 2$ and Mohit’s age would be $y - 2$. It is given that Mohit’s age was thrice his son’s age. That means,
\[ \Rightarrow \] \[y - 2 = 3(x - 2)\]
\[ \Rightarrow y - 3x = - 4\] $...\left( 1 \right)$
The second timeline is two years from the present. The son of Mohit has an age of $x + 2$ years then and Mohit, the father, has an age of $y + 2$ years. It is provided in the above given question that Mohit, the father’s age will be five times that of his son. That means,
\[ \Rightarrow \]$2(y + 2) = 5(x + 2)$
$ \Rightarrow 2y + 4 = 5x + 10$
$ \Rightarrow 2y - 5x = 6$ $...\left( 2 \right)$
From the two equations, we can eliminate $y$ to find the value of $x$ ;
\[ \Rightarrow \]$3x - 4 = \dfrac{{5x + 6}}{2}$
\[ \Rightarrow \]$6x - 8 = 5x + 6$
\[ \Rightarrow \]$x = 14$
Therefore, the value of y is,
\[ \Rightarrow \] y - 3x = - 4
\[ \Rightarrow \]y = 3x - 4 = 3 $\times$ 14 - 4 = 38
Therefore,

Mohit’s current age is $38$ years old which is option (B).

Note: We can also take Mohit’s age as the reference point and solve for son’s age. But this would lead to a lot of complicated calculations with fractions and isn’t that feasible an option.