The age of the father is twice the sum of the ages of his two children. After 20 years, his age will be equal to the sum of the ages of his children. Find the age of the father.

Given:

The age of the father is twice the sum of the ages of his two children. After 20 years, his age will be equal to the sum of the ages of his children.

To do:

To find the present age of the father.

Solution:

Let the sum of two sons' present ages be $x$ years.

This implies,

Father's age$=2x$.....(i)

After 20 years,

The sum of the sons' ages $=( x+20+20)=x+40$

Father's age $=2x+20$

According to the given question,

$2x+20=(x+40)$

$\Rightarrow 2x+20=x+40$

$\Rightarrow 2x-x=40-20$

$\Rightarrow x=20$ years

Therefore,

Father's age $2x=2\times20=40$ years.

The age of the father is 40 years.

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