Question

47. 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 father.​

Answer 1

Answer:

Age of his father = 45 years

Step-by-step explanation:

given that,

A father's age is three times the sum of the ages of his two children.

let the age of father be x

and the sum of ages of his two children be y

so,

According to the question,

y = 3(x)

3x = y

3x - y = 0 .....(1)

now,

also given that,

After 5 years his age will be two

times the sum of their ages

so,

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

[ages of two children]

y + 5 = 2x + 20

2x - y = 5 - 20

2x - y = -15. ....(2)

now,

we have,

3x - y = 0 .....(1)

2x - y = -15. ....(2)

substracting (2) from (1)

3x - y - (2x - y) = 0 - (-15)

3x - y - 2x + y =15

x = 15

from (1)

3x - y = 0

3(15) - y = 0

-y = -45

y = 45

so,

Age of his father = 45 years

Answer 2

Answer:

Step-by-step explanation:

Given :-

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.

To Find :-

Present age of father

Solution :-

Let the sum of ages of two sons be x years

Age of father = 3x years

After 5 years

Age of the fathers become = (3x + 5) years

Sum of ages of two sons becomes = (x + 10) years

So the equations becomes

⇒ (3x + 5) = 2(x + 10)

⇒ (3x + 5) = 2x + 20

⇒ 3x - 2x = 20 -5

⇒ x = 15  years.

Sons Age = 15 years

Putting x value in Father's age

3x = 3(15) = 45  years

Hence, the age of the father is 45 years.