Question

Ten years ago the age of a father was four times of his son. Ten years hence the age of the father will be twice that of his son.The present ages of the father and the son​

Answer 1

Here is the correct solution for this problem.

Answer 2

$\mathfrak{\large{\underline{\underline{Answer :-}}}}$

The father is 50 years old and Son is 20 years old.

$\mathfrak{\large{\underline{\underline{Explanation :-}}}}$

Given :

10 years ago = Father was four times his son

10 years hence = father will be twice that of his son.

To find :

Their present ages

Solution :

Consider the age of father as y and sons age as x

⛤ 10 years ago = Father was four times his son

⟹ y - 10 = 4(x - 10)

⟹ y - 4x = -30

⟹ x = 4y - 30 .......................[1]

⛤ 10 years hence = father will be twice that of his son.

⟹ y + 10 = 2(x+10)

⟹ y + 10 = 2x + 20

⟹ y = 2x + 10 .....................[2]

⛤ We need to equate [1] and [2]

⟹ 4x - 30 = 2x + 10

⟹ 4x - 2x = 10 + 30

⟹ 2x = 40

⟹ x = 40/2

⟹ x = 20

x = 20 years

⛤ Place the value of x in Equation [2]

⟹ y = (2 × 20) + 10

⟹ y = 40 + 10

⟹ y = 50

y = 50 years

$\therefore$ The father is 50 years old and Son is 20 years old.