Question

# Father 's age is three times the sum of the ages of his two children. After 5 years his age will be twice thesum of ages of two children. Find the age of father.

Hint:- Here we go through by supposing the age of father be x year and the sum of the age of children be y then solving accordingly to the question for finding the value of x and y.

Let the age of father =x years
The sum of the age of 2 children =y years
According to the first condition,
The age of father is thrice the sum of age of his two children.
$\Rightarrow$ x=3y.....let it equation (1)
After 5 years
$\Rightarrow$Father 's age =x+5
$\Rightarrow$The sum of the ages of his two children =y+10 (Here we add 10 because y is the sum of
the age of two children so we add 5 in both the children so it becomes 10).
According to the second condition,
The age of a father became twice the sum of the age of his two children.
$\Rightarrow$x+5=2(y+10)
$\Rightarrow$x+5=2y+20
$\Rightarrow$x−2y=15 ……let it be equation (2)
Put the value of x from equation 1
$\Rightarrow$3y−2y=15
$\Rightarrow$y=15
Put y=15 in equation 1.

$\Rightarrow$x=3×15
$\Rightarrow$x=45
$\therefore$The age of the father that we let x is 45 years and the sum of the age of his children that we let y be 15 years.

Note: - Whenever we face such a type of question on age problems first always suppose the present age in some variables and then apply the conditions of question on that variable to find out the value of that variable to find out the result.