Father’s age is three times the sum of ages of his two children. After 5 years his age will be twice the sum of ages of two children. Find the age of father.
Given:
A father's age is three times the sum of the ages of his two children. After 5 years his age will be twice the sum of the ages of two 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$=3x$.....(i)
After 5 years,
The sum of the sons' ages $=( x+10)$
Father's age $=3x+5$
According to the given question,
$3x+5=2(x+10)$
$\Rightarrow 3x+5=2x+20$
$\Rightarrow 3x-2x=20-5$
$\Rightarrow x=15$ years
Therefore,
Father's age $3x=3\times15=45$ years.
The age of the father is 45 years.
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