Question

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.

Answer 1

Let us assume, the present age of Father is x years
and the ages of his sons are a, b years respectively.

Given:

x = 3 (a + b) ---------------------1

Also given, after 5 years,

x + 5 = 2 (a + 5 + b + 5)
x + 5 = 2 (a + b + 10)
x + 5 = 2 (a + b) + 20
x = 2 (a + b) + 15

Substitute the value of x from equation 1 

3 (a+b) = 2 (a+b) + 15
a + b = 15

Therefore, x = 3 (a + b) = 3 * 15 = 45

Answer - The present age of father is 45 years.

Answer 2

$\mathfrak{\huge{Answer:}}$

Let age of father = x

Let sum of the ages of the two children be = y

According to the question :-

x = 3y ....(1)

---After 5 years, ages will be----

Father's age = x + 5

Sum of the two children = y + 5 + 5 ( since this "y" comprises ages of two people, the addition needs to be done twice )

According to the question :-

x + 5 = 2 ( y + 10 )

=》 x + 5 = 2y + 20

Due to (1)

=》 3y + 5 = 2y + 20

=》 y = 15

Age of father = 3y = 3 × 15 = 45 years