Question

2. The age of the 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 his children. Find the present ages of the
father​

Answer 1

Answer:

Step-by-step explanation:

A father’s age is three times the age of his two sons. After 5 years, his age will be twice the sum of the ages of his sons. What is the age of the father?

Answer : Let the age of the sons be x and y.

Given that Father’s age is three times the age of his two sons.

Therefore, present age of father is 3(x+y)

Now, it is also given, after 5 years, his age will be twice the sum of the ages of his son.

Therfore, after 5 years age of father will be 3(x+y)+5 and age of the sons will be x+5 and y+5.

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

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

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

3x-2x+3y-2y = 20–5

x+y = 15

Now the age of father was 3(x+y)=3(15)=45 (Putting the value of x+y)

Thus the age of the father is 45.

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Answer 2

$\Large\underline\mathbf{Given:-}$

• Age of the 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 his children.

$\Large\underline\mathbf{To \: Find:-}$

• What is the present age of Father ?

$\Large\underline\mathbf{Solution:-}$

Let the present ages of children be 'x' and 'y' years

⁂ Sum of ages of his two children = (x + y) years

CASE:- 1)

➣ Age of the father is three times the sum of ages of his two children.

• Age of Father = 3(x + y) years

CASE:- 2)

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

• Father's age = 3(x + y ) + 5 years
• Sum of ages of two children = (x + 5 + y + 5) years

【Father's age = 2(Sum of ages of children)】

${\underline{\bf{According \: To \: Question:-}}}$

➜ 3(x + y) + 5 = 2(x + y + 10)

➜ 3x + 3y + 5 = 2x + 2y + 20

➜ 3x + 3y –2x –2y = 20 –5

➜ x + y = 15

⁂ Sum of ages of his two children = 15

⁂ Father's age = 3(x + y)

➜ Father's age = 3 $\times$ 15

$\bf{\star \: Father's \: age = 45 \: years\: \star}$

❝ Hence, the age of Father is 45 years ❞

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