Question

The sum of two children is 'a'. The age of the father is twice the 'a'. After twenty years, his age will be equal to
he addition of the ages of his children. Find the age of father.
​

Answer 1

Answer:

......................

Answer 2

Answer :

40 years

Solution :

• Let s and s' be the present ages of two children .

• Let f be the present age of the father .

Now ,

According to question , the sum of two children is a .

Thus ,

s + s' = a --------(1)

Also ,

The age of father is twice a .

Thus ,

f = 2a ---------(2)

Now ,

• After 20 years , the sum of ages of children will be (s + 20) and (s' + 20) .

• After 20 years , the age of father will be (f + 20) .

But ,

According to the question , after 20 years father's age will be equal to the ages of his children .

Thus ,

=> (s + 20) + (s' + 20) = f + 20

=> s + s' + 20 + 20 = f + 20

=> a + 20 = f { using eq-(1) , s + s' = 20 }

=> f = a + 20 ----------(3)

Now ,

From eq-(2) and (3) , we have ;

=> 2a = a + 20

=> 2a - a = 20

=> a = 20

Now ,

Using eq-(2) , we have ;

=> f = 2a

=> f = 2 × 20

=> f = 40

Hence ,

Present age of father is 40 years .