The present age of a father is three years more than three times the age of the son. Three years hence father’s age will be 10 years more than twice the age of the son. Determine their present ages.

Given :

The present age of a father is three years more than three times the age of the son. Three years hence father’s age will be 10 years more than twice the age of the son.

To find :

We have to find their present ages.

Solution : 

Let the present age of the son be $x$.

This implies,

The age of the father $= (3\times x)+3=3x+3$

Age of the son after 3 years $= x+3$

Age of the father after 3 years $= (3x+3)+3=3x+6$.

After three years father’s age will be 10 years more than twice the age of the son.

Therefore,

$3x+6 = 2(x+3)+10$

$3x+6 = 2x+6+10$

$3x-2x = 16-6$

$x = 10$

$\Rightarrow 3x+3=3(10)+3=30+3=33$ years

The present age of the son is $10$ years and the present age of the father is $33$ years.  

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Updated on: 10-Oct-2022

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