Question

Manick is \[12\] years old and is three times as old as his brother Rahul. How old will Manick be when he is twice as old as Rahul?
(A) $14$years (B) $16$years (C) $18$years (D) $20$years

Answer 1

Hint: Find the present age of Rahul and then determine after how many years he will be half the age of his brother by forming a linear equation.
It is given in the question that the present age of Manick is \[12\] years old and his age is thrice the age of his brother Rahul.
$\therefore $Then, the present age of Rahul $ = \dfrac{{12}}{3} = 4$years old.
We have to find the age of Manick when he will be twice the age of Rahul. So, after $y$more years his age will be twice that of Rahul. Then we’ll get:
Manick’s age after $y$years$ = 12 + y$,
and Rahul’s age after $y$years $ = 4 + y$
Then, according to the above condition, we have:
$
   \Rightarrow 12 + y = 2 \times \left( {4 + y} \right), \\
   \Rightarrow 12 + y = 8 + 2y, \\
   \Rightarrow y = 4 \\
$
Thus, after $4$years Manick will be twice as old as Rahul. Consequently Manick’s age after $4$ years will be $12 + 4 = 16$ years old. (B) option is correct.
Note: We can also solve the problem by basic aptitude method without forming any equation. As it is clear from the first statement that Rahul’s present age is $4$ years old. And although Manick’s present age is $12$ years old, after a few years his age will be twice as that of Rahul. Thus, his age will be an even number then also. Now, we can hit and trial for a few even numbers after $12$ to get our desired result. More complex problems of such type may lead us to form and solve simultaneous equations.