A father’s age is three times the sum of the ages of his two children. After 5 years his age will be two times the sum of their ages. Find the present age of the father.

Or

A fraction becomes 1/3 when 2 is subtracted from the numerator and it becomes 1/2 when 1 is subtracted from the denominator. Find the fraction.

Let, the present age of the father is x and the age of two children be x₁ and x₂.

According to the question, the father’s age is three times the sum of the ages of his two children.

⇒ x = 3(x₁ + x₂) …(1)

According to the question after 5 years the father's age will be two times the sum of their ages.

x + 5 = 2(x₁ + 5 + x₂ + 5)

⇒ x + 5 = 2(x₁ + 5 + x₂ + 5)

⇒x = 2(x₁ + x₂) + 15 …(2)

Equate eq (1) and (2) to get,

⇒3(x₁ + x₂)  = 2(x₁ + x₂) + 15

⇒(x₁ + x₂) = 15

Put this value in (1) to get,

⇒x = 3(15)

⇒ x = 45

So, present age of father is 45 years.

OR

Let, be the fraction.

According to the question, a fraction becomes 1/3 when 2 is subtracted from the numerator.

⇒ 3(p – 2) = q …(1)

⇒ 2p = q – 1

⇒ 2p + 1 = q…(2)

equate (1) and (2),

⇒3(p – 2) = 2p + 1

⇒3p - 6 = 2p + 1

⇒p = 7

So, p = 7 and q = 15

Hence, the fraction is .