Question

Two years ago, father was three times as old as his son and two years hence, twice his age will be equal to five times that of his son.Find their present ages​

Answer 1

Given :

• Two years ago, father was three times as old as his son.
• Two years hence, twice his age will be equal to five times that of his son.

To find :

• Present age of Father and Son

Solution :

Let,

• Present age of son = x years
• Present age of father = y years

Two years ago,

• Age of son = x - 2 years
• Age of father = y - 2 years

According to the question,

→ y - 2 = 3(x - 2)

→ y - 2 = 3x - 6

→ y - 3x = - 6 + 2

→ y - 3x = - 4 ------(1)

Two years hence,

• Age of son = x + 2 years
• Age of father = y + 2 years

According to the question,

→ 2(y + 2) = 5(x + 2)

→ 2y + 4 = 5x + 10

→ 2y - 5x = 10 - 4

→ 2y - 5x = 6 -----(2)

Taking (1) and (2)

→⠀(y - 3x = - 4) × 2

→⠀(2y - 5x = 6) × 1

→ 2y - 6x = - 8 ----(3)

→ 2y - 5x = 6 -------(4)

Solving (3) and (4).

⠀⠀⠀⠀⠀⠀⠀⠀⠀2y - 6x = - 8

⠀⠀⠀⠀⠀⠀⠀⠀⠀2y - 5x = 6

⠀⠀⠀⠀⠀⠀⠀⠀⠀- ⠀+ ⠀⠀ -

⠀⠀⠀⠀⠀⠀⠀______________

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀- 1x = - 14

⠀⠀⠀⠀⠀⠀⠀______________

→ - 1x = - 14

→ x = 14

The value of x = 14

Substitute the value of x in (1).

→ y - 3x = - 4

→ y - 3(14) = - 4

→ y - 42 = - 4

→ y = - 4 + 42

→ y = 38

The value of y = 38.

Therefore,

• Present age of Son = x = 14 years
• Present age of Father = y = 38 years