Question

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

Answer 1

✬ Father's Age = 45 Years ✬

Step-by-step explanation:

Given:

• Father age is three times the sum of ages of his two children.
• 5 years later father's age will be two times the sum of ages of his children.

To Find:

• What is the present age of father ?

Solution: Let the ages of his two children be x and y. Therefore,

➟ Present age of father = 3(sum of x + y)

➟ Present age of father = 3(x + y)....(1)

[ Now, after 5 years their ages will be ]

• 1st children age = (x + 5) years
• 2nd children age = (y + 5) years
• Father's age = 3(x +y) + 5 years

A/q

• 5 years later father's age will be two times the sum of ages of his children.

$\implies{\rm }$ 3(x + y) + 5 = 2(x + 5 + y + 5)

$\implies{\rm }$ 3x + 3y + 5 = 2(10 + x + y)

$\implies{\rm }$ 3x + 3y + 5 = 20 + 2x + 2y

$\implies{\rm }$ 3x – 2x + 3y – 2y = 20 – 5

$\implies{\rm }$ x + y = 15.....(1)

So, present age of father is

➙ 3(x + y)

➙ 3(15) { from equation 1 }

➙ 45 years

Hence, Present age of father is 45 years.

Answer 2

Step-by-step explanation:

$\bf{\underline{\underline\red{Given:-}}}$

• The age of father is three times the sum of ages of his two children.

• After 5 years his age will be two times the sum of the ages of children.

$\bf{\underline{\underline\blue{To\:Find:-}}}$

• The present age of father.

$\bf{\underline{\underline\green{Solution:-}}}$

Let the age of father be x

And sum of ages of his two children be y

According to the 1st condition:-

The age of father is three times the sum of ages of his two children.

So:-

$\rm\implies x = 3y......(i)$

According to 2nd condition:-

After 5 years his age will be two times the sum of the ages of children.

After 5 years

Age of father = (x + 5)

Sum of ages of his two children = y + 10

He will be two twice the sum of ages of his children.

$\rm\implies x + 5= 2(y + 10)$

$\rm\implies x + 5= 2y +20$

$\rm\implies x - 2y = 20 - 5$

$\rm\implies x - 2y = 15.....(ii)$

Substituting equation (i) in (ii)

$\rm\implies 3y - 2y = 15$

$\rm\implies y = 15$

Substituting y = 15 in equation (ii)

$\rm\implies x - 2y = 15$

$\rm\implies x - 2(15) = 15$

$\rm\implies x -30 = 15$

$\rm\implies x = 15 + 30$

$\rm\implies x = 45$

$\underline{\boxed{\rm \purple{\therefore The \: presen t \: age \: of \: father \: = 45 \: years}}}$