The present age of a man is 2 years more than five times the age of hi

1.	The present age of a man is 2 years more than five times the age of his son. Two years hence, the man’s age will be 8 years more than three times the age of his son. Find their present ages.
Answer» Let the man’s present age be x years. Let his son’s present age be y years. According to the question, we have: Two years ago: Age of the man = Five times the age of the son ⇒ (x – 2) = 5(y – 2) ⇒ x – 2 = 5y – 10 ⇒ x – 5y = –8 …….(i) Two years later: Age of the man = Three times the age of the son + 8 ⇒ (x + 2) = 3(y + 2) + 8 ⇒ x + 2 = 3y + 6 + 8 ⇒ x – 3y = 12 …………(ii) Subtracting (i) from (ii), we get: 2y = 20 ⇒ y = 10 On substituting y = 10 in (i), we get: x – 5 × 10 = -8 ⇒ x – 50 = -8 ⇒ x = (-8 + 50) = 42 Hence, the present age of the man is 42 years and the present age of the son is 10 years.

The present age of a man is 2 years more than five times the age of his son. Two years hence, the man’s age will be 8 years more than three times the age of his son. Find their present ages.

Answer»

Let the man’s present age be x years.

Let his son’s present age be y years.

According to the question, we have:

Two years ago:

Age of the man = Five times the age of the son

⇒ (x – 2) = 5(y – 2)

⇒ x – 2 = 5y – 10

⇒ x – 5y = –8 …….(i)

Two years later:

Age of the man = Three times the age of the son + 8

⇒ (x + 2) = 3(y + 2) + 8

⇒ x + 2 = 3y + 6 + 8

⇒ x – 3y = 12 …………(ii)

Subtracting (i) from (ii), we get:

2y = 20

⇒ y = 10

On substituting y = 10 in (i), we get:

x – 5 × 10 = -8

⇒ x – 50 = -8

⇒ x = (-8 + 50) = 42

Hence, the present age of the man is 42 years and the present age of the son is 10 years.