Question

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.

• A. $30$ years
• B. $35$ years
• C. $40$ years
• D. $22$ years

Answer 1

The correct option is C $40$ years

Let the age of father be $x$ years

Let the age of one of his children be $y$ years and age of other children be $z$ years

From given information,

$x=2\times (y+z)$ ......(1)

After $20$ years,

$(x+20)=(y+20)+(z+20)$ .......(2)

Substituting value of (1) in (2), we get

$2\times (y+z)$ $+20=y+z+40$

$2y+2z-y-z=40-20$

$y+z=20$ ......(3)

Substituting value of (3) in (1), we get

$x=2\times \left(20\right)$

$\Rightarrow x=40$

Age of father is $40$ years.