# I am three times as old as my son. Five years later, I shall be two and half times as old as my son. How old am I and how old is my son?

Last updated date: 23rd Mar 2023

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Answer

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Hint: Solve the problem by first converting into algebraic equations.

Let my age be $x$ years and my son’s age be $y$ years.

Then at present, $x = 3y$ --- (1)

Five years later,

My age will be $\left( {x + 5} \right)$ and my son’s age will be $\left( {y + 5} \right)$ years.

From the statement given in question for 5 years later, we have

$

\Rightarrow \left( {x + 5} \right) = \left( {2 + \dfrac{1}{2}} \right)\left( {y + 5} \right) \\

\Rightarrow \left( {x + 5} \right) = \left( {\dfrac{5}{2}} \right)\left( {y + 5} \right) \\

\Rightarrow 2x + 10 = 5y + 25 \\

\Rightarrow 2x - 5y - 15 = 0 \\

$ ---- (2)

Putting the value of $x$ from equation (1) into equation (2), we get

$

\Rightarrow 2\left( {3y} \right) - 5y - 15 = 0 \\

\Rightarrow y = 15 \\

$

From equation (1)

$

x = 3y \\

x = 3 \times 15 \\

x = 45 \\

$

Hence, my present age is 45 years and my son’s present age is 15 years.

Note: - In these types of problems, reduce the data in the problem statement in terms of variables. Generate equations based on the conditions given in the problem statements. Then solve those equations to determine the values of the variables.

Let my age be $x$ years and my son’s age be $y$ years.

Then at present, $x = 3y$ --- (1)

Five years later,

My age will be $\left( {x + 5} \right)$ and my son’s age will be $\left( {y + 5} \right)$ years.

From the statement given in question for 5 years later, we have

$

\Rightarrow \left( {x + 5} \right) = \left( {2 + \dfrac{1}{2}} \right)\left( {y + 5} \right) \\

\Rightarrow \left( {x + 5} \right) = \left( {\dfrac{5}{2}} \right)\left( {y + 5} \right) \\

\Rightarrow 2x + 10 = 5y + 25 \\

\Rightarrow 2x - 5y - 15 = 0 \\

$ ---- (2)

Putting the value of $x$ from equation (1) into equation (2), we get

$

\Rightarrow 2\left( {3y} \right) - 5y - 15 = 0 \\

\Rightarrow y = 15 \\

$

From equation (1)

$

x = 3y \\

x = 3 \times 15 \\

x = 45 \\

$

Hence, my present age is 45 years and my son’s present age is 15 years.

Note: - In these types of problems, reduce the data in the problem statement in terms of variables. Generate equations based on the conditions given in the problem statements. Then solve those equations to determine the values of the variables.

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