Question

Two Years Ago A Man Was 6 Times as old as his son. After 18 years he will be twice as old as his son.
What will be the preseent age of the father and the son​

Answer 1

here is ur answer see the attachment

present age of father is 32 years

present age of son is 7 years

Answer 2

Let us assume that the present age of man be x years and the present age of his son be y years.

“Two years ago a man was 6 times as old as his son.”

Two years ago, the age of man = (x - 2) years

Two years ago, the age of son = (y - 2) years

According to question,

⇒ (x - 2) = 6(y - 2)

⇒ x - 2 = 6y - 12

⇒ x - 6y = -12 + 2

⇒ x - 6y = - 10

⇒ x = 6y - 10

Also, “After 18 years he will be twice as old as his son.”

After 18 years, the age of man = (x + 18) years

And the age of son = (y + 18) years

According to question,

⇒ (x + 18) = 2(y + 18)

⇒ x + 18 = 2y + 36

Substitute value of x from above

⇒ 6y - 10 + 18 = 2y + 36

⇒ 6y + 8 = 2y + 36

⇒ 6y - 2y = 36 - 8

⇒ 4y = 28

⇒ y = 7

Substitute value of y in x

⇒ x = 6(7) - 10

⇒ x = 42 - 10

⇒ x = 32

Therefore,

The present age of a man is 32 years and his son is 7 years.