Question

The age of a man is twice the sum of the ages of his two children. After 20 years. his age will he equal to the sum of the ages of his children at that time. Find the present age of the man.

If at present :
Man's age = x years and sum of the ages of two children = y years Then x = 2y

In 20 years :
Age of each child increases by 20 years
$\Rightarrow$ in 20 years. ages of both the children will increase by (20 + 20) years.
$\therefore x+20=y+20+20$

Answer 1

Let the fathers age be x yrs
the sum of ages of 2 children be (a+b)yrs
acc to 1st condition
x=2(a+b)=2a+2b.....(1)
acc to 2nd condition
x+20=a+20+b+20
x+20=a+b+40
x=a+b+20.....(2)
equating (1) & (2)
a+b=20
sub this in(1)
x=40
therefore the fathers age is 40 yrs.