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# Rahul is 34 years old and Anuj is 15 years old. After how many years will the age of Rahul be twice that of Anuj?

Last updated date: 14th Jul 2024
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Hint: Type of question is based on the age problems, also that they are based on the linear equation in one variable. For this concept says we had to assume that after some years they will be equal to what is asked in the question, (as in our case they asked to be twice) then equate them by though the means of addition, subtraction, multiplication or division whichever is possible according to the question, which on further simplifying we will get the answer.

Complete step-by-step solution:
In our case we have two boys name as Rahul and anuj with age of 34 and 15 respectively, and asked that after how many years Rahul will be twice that of anuj, so we will assume that years and equate both of them by multiplying the anuj by 2, from where we will get equation in one variable and on further simplifying we will get the years, after which Rahul will be twice of Anuj.
So moving ahead with the question;
Rahul’s age$=34$
Anuj’s age$=15$
Let; after ‘t’ years Rahul will be twice that of anuj; So
Rahul’s age after t years$=34+t$
Anuj’s age after t years$=15+t$
So we can say that after t years if we multiply Anuj's age by 2 then we will get that value equal to Rahul’s age. So we can write it as after t years;
\begin{align} & \text{Rahuls age}=2\times \text{Anujs age} \\ & 34+t=2\left( 15+t \right) \\ &\Rightarrow 34+t=30+2t \\ &\Rightarrow t=4 \\ \end{align}
Hence answer is 4 i.e. after 4 years Rahul’s age will be twice that of Anuj’s age.

Note: For the type of question we just had to find any relation between the values, on further solving we will get the answer. Moreover, as we had multiplied by two in the Anuj’s age, rather than this if we divide Rahul’s age by two then also we can equate both.