Question

the age of father is twice is the sum of age of his 2 children. after 20 years his age will be equal to the sum of the age of his children. find the age of the following​

Answer 1

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Answer 2

Corrected Question :

» The age of father is twice the sum of age of his 2 children. After 20 years his age will be equal to the sum of the age of his children. find the age of father and sum of age of his two children.

Given :

• Age of father is twice the sum of age of his 2 children.

• After 20 years the age of father will be equal to the sum of the age of his children.

To find :

• Age of father and his two children

Solution :

Let,

• The present age of father = x years
• The sum of age his 2 children = y years

According to the first condition given,

⟶ Age of father = 2(Sum of age of his 2 children)

⟶ x = 2y

⟶ x - 2y = 0 -----(1)

Their ages after 20 years,

⟶ Age of father = x + 20 years

⟶ Sum of age of his 2 children = y + 20 + 20

⟶ Sum of age of his 2 children = y + 40 years

According to the second condition,

⟶ Father's age = Sum of age of his children

⟶ x + 20 = y + 40

⟶ 20 - 40 = y - x

⟶ - 20 = - x + y ------(2)

Solving (1) and (2) :-

x - 2y = 0

-x + y = - 20

_____________

- y = - 20

_____________

⟶ - y = - 20

⟶ y = 20

Substitute the value of y in equation 1 :-

⟶ x - 2y = 0

⟶ x - 2(20) = 0

⟶ x - 40 = 0

⟶ x = 40

Therefore,

• Present age of father = x = 40 years
• Sum of age of his 2 children = y = 20 years