# 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

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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.

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.

Last updated date: 28th Sep 2023

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