# Raju is 5 years younger than Rahul. Four years later Rahul will be twice as old as Raju. Find the present ages.

Last updated date: 19th Mar 2023

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Answer

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Hint – In this question the relationship between the ages of Raju and Rahul is given to us and we need to find their present ages so let their present ages be some variable and use these relations to obtain mathematical equations in two variables. This will help you get the answer.

Complete step-by-step answer:

Let the age of Raju be x years.

And the age of Rahul is y years.

Now it is given that Raju is 5 years younger than Rahul.

Now construct the linear equation according to given information we have,

Age of Raju is equal to the age of Rahul minus five.

$ \Rightarrow x = y - 5$…………………….. (1)

Now it is also given that four years later Rahul will be twice as old as Raju.

Now again construct the linear equation according to given information we have,

$ \Rightarrow y + 4 = 2\left( {x + 4} \right)$…………………….. (2)

Now put the value of x from equation (1) in equation (2) we have,

$ \Rightarrow y + 4 = 2\left( {y - 5 + 4} \right)$

Now simplify the above equation we have,

$

\Rightarrow y + 4 = 2\left( {y - 1} \right) \\

\Rightarrow y + 4 = 2y - 2 \\

\Rightarrow 2y - y = 4 + 2 \\

$

$ \Rightarrow y = 6$ Years.

Now put the value of y in equation (1) we have,

$ \Rightarrow x = 6 - 5 = 1$

So, the age of Raju is 1 year and the age Rahul is 6 years.

So, this is the required answer.

Note – Whenever we face such types of problems the key concept is simply to formulate equations involving two variables using the information provided in the question. Use the concept of variable evaluation to have two variables either by using elimination or substitution, this will help you get on the right track to reach the answer.

Complete step-by-step answer:

Let the age of Raju be x years.

And the age of Rahul is y years.

Now it is given that Raju is 5 years younger than Rahul.

Now construct the linear equation according to given information we have,

Age of Raju is equal to the age of Rahul minus five.

$ \Rightarrow x = y - 5$…………………….. (1)

Now it is also given that four years later Rahul will be twice as old as Raju.

Now again construct the linear equation according to given information we have,

$ \Rightarrow y + 4 = 2\left( {x + 4} \right)$…………………….. (2)

Now put the value of x from equation (1) in equation (2) we have,

$ \Rightarrow y + 4 = 2\left( {y - 5 + 4} \right)$

Now simplify the above equation we have,

$

\Rightarrow y + 4 = 2\left( {y - 1} \right) \\

\Rightarrow y + 4 = 2y - 2 \\

\Rightarrow 2y - y = 4 + 2 \\

$

$ \Rightarrow y = 6$ Years.

Now put the value of y in equation (1) we have,

$ \Rightarrow x = 6 - 5 = 1$

So, the age of Raju is 1 year and the age Rahul is 6 years.

So, this is the required answer.

Note – Whenever we face such types of problems the key concept is simply to formulate equations involving two variables using the information provided in the question. Use the concept of variable evaluation to have two variables either by using elimination or substitution, this will help you get on the right track to reach the answer.

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