Let the age of a man = x years
And the age of his son = y years
Ten years hence,
Man’s age = (x + 10) years
Son’s age = (y + 10) years
According to the question,
(x + 10) = 2(y + 10)
⇒ x + 10 = 2y + 20
⇒ x = 2y + 20 – 10
⇒ x = 2y + 10 ...(i)
Ten years ago,
Father’s age = (x – 10) years
Son’s age = (y – 10) years
According to the question,
(x – 10) = 4(y – 10)
⇒ x – 10 = 4y – 40
⇒ x = 4y – 30 …(ii)
From Eq. (i) and (ii), we get
2y + 10 = 4y – 30
⇒ 2y – 4y = – 30 – 10
⇒ – 2y = – 40
⇒ y = 20
On putting the value of y = 20 in Eq. (i), we get
x = 2y + 10
⇒ x = 2(20) + 10
⇒ x = 50
Hence, the age of man is 50 years and the age of his son is 20 years.