# Present age of Pranesh is four times the age of his son. Five years ago, the sum of their ages was 50 years. What is the present age of Pranesh?

Last updated date: 17th Mar 2023

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Answer

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Hint – In the question the relation between the ages of Pranesh and his son is given to us changing respectively as age changes with time. So use these relations provided to formulate mathematical equations by assuming variables to the age of Pranesh and his son.

Complete step-by-step answer:

Let the present age of Pranesh be x years.

And the present age of his son is y years.

Now it is given that the present age of Pranesh is four times the age of his son.

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

Age of Pranesh is equal to 4 multiplied by the age of his son.

$ \Rightarrow x = 4y$…………………….. (1)

Now it is also given that five years ago the sum of their ages was 50 years.

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

$ \Rightarrow \left( {x - 5} \right) + \left( {y - 5} \right) = 50$…………………….. (2)

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

$ \Rightarrow 4y - 5 + y - 5 = 50$

Now simplify the above equation we have,

$ \Rightarrow 5y = 60$

Now divide by 5 we have,

$ \Rightarrow y = 12$ Years.

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

$ \Rightarrow x = 4\left( {12} \right) = 48$ Years.

So, the present age of Pranesh is 48 years and the present age of his son is 12 years.

So, this is the required answer.

Note – Whenever we face such types of problems the key concept here is to simply formulate the mathematical questions generally of two variables in most of the cases. Then use methods of variable evaluation like elimination or substitution. This concept will help you get on the right track to get the answer.

Complete step-by-step answer:

Let the present age of Pranesh be x years.

And the present age of his son is y years.

Now it is given that the present age of Pranesh is four times the age of his son.

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

Age of Pranesh is equal to 4 multiplied by the age of his son.

$ \Rightarrow x = 4y$…………………….. (1)

Now it is also given that five years ago the sum of their ages was 50 years.

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

$ \Rightarrow \left( {x - 5} \right) + \left( {y - 5} \right) = 50$…………………….. (2)

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

$ \Rightarrow 4y - 5 + y - 5 = 50$

Now simplify the above equation we have,

$ \Rightarrow 5y = 60$

Now divide by 5 we have,

$ \Rightarrow y = 12$ Years.

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

$ \Rightarrow x = 4\left( {12} \right) = 48$ Years.

So, the present age of Pranesh is 48 years and the present age of his son is 12 years.

So, this is the required answer.

Note – Whenever we face such types of problems the key concept here is to simply formulate the mathematical questions generally of two variables in most of the cases. Then use methods of variable evaluation like elimination or substitution. This concept will help you get on the right track to get the answer.

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