Question

If father age is three times the sum of his two children after 5 years his age will be two times the sum of their ages find the present age of his father

Answer 1

Answer:-

Let the sum of the ages of two children be "C" and Father's age be "F".

Father's age = 3*C = 3C

F = 3C -- equation (1)

After five years,

Sum of ages of the children = C + 2(5) [ 2 represents the number of children ]

Sum of ages of the children = 10 + C.

Father's age is twice the sum of ages of the children.

Hence, F + (1)5 = 2( C + 10)

F + 5 = 2C + 20

F = 2C - 5 + 20

F = 2C + 15 -- equation (2)

Equate both the situations,

3C = 2C + 15

3C - 2C = 15

C = 15

Substitute "C" value in equation (1)

F = 3C

F = 3(15)

F = 45

Hence, the present age of father is 45 years.

Answer 2

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

Given:

Father's age is three times the sum of his two children and after 5 years his age will be two times the sum of their ages.

To Find:

The present age of father.

Solution:

Let us assume that the age of two children is x and y respectively.

According to the question, father's age is three times the sum of the ages of his children = 3 ( x + y ).

After 5 years,

Age of children = ( x + 5 ) + ( y + 5 )

= x + y + 10

Now, age of father after 5 years =

2 ( x + y + 10) = 3 ( x + y ) + 5

2x + 2y + 20 = 3x + 3y + 5

2x - 3x + 2y - 3y = 5 - 20

-x -y = -15

- ( x + y ) = -15

or x + y = 15

Now, father's age = 3 × ( x + y ) = 3 × (15 ) = 45

Therefore father's age is 45 years.