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# A Father’s age is three times the sum of the ages of his two children After 5 years his age will be two times the sum of their ages. find the present age of the father?

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This is the Important question based on Linear Equations in two Variables Chapter of R.S Aggarwal book for
ICSE & CBSE Board.
Question Number 50 Exercise 3E of RS Aggarwal Solution.
In this Question following Points are given.
(i)Father’s age is three times the sum of the ages of his two children.
(ii)After 5 years his age will be two times the sum of their ages.
You have to find the present age of the father.

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1. Let the age of the sons be x and y.
Given that Father’s age is three times the age of his two sons.
Therefore, present age of father is 3(x+y)
Now, it is also given, after 5 years, his age will be twice the sum of the ages of his son.
Therfore, after 5 years age of father will be 3(x+y)+5 and age of the sons will be x+5 and y+5.
3(x+y)+5 = 2(x+5+y+5)
3x+3y+5 = 2x+10+2y+10
3x+3y+5 = 2x+2y+20
3x-2x+3y-2y = 20–5
x+y = 15
Now the age of father was 3(x+y)=3(15)=45 (Putting the value of x+y)
Thus the age of the father is 45.

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