Answer :

Let, the present age of the father is x and the age of two children be x_{1 }and x_{2}.

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

⇒ x = 3(x_{1} + x_{2}) …(1)

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

x + 5 = 2(x_{1} + 5 + x_{2} + 5)

⇒ x + 5 = 2(x_{1} + 5 + x_{2} + 5)

_{1}+ x

_{2}+ 10)

⇒ x + 5 = 2(x

_{1}+ x

_{2}) + 20

⇒x = 2(x_{1} + x_{2}) + 15 …(2)

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

⇒3(x_{1} + x_{2}) = 2(x_{1} + x_{2}) + 15

⇒(x_{1} + x_{2}) = 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)

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

⇒ 2p = q – 1

⇒ 2p + 1 = q…(2)

equate (1) and (2),

⇒3(p – 2) = 2p + 1

⇒3p - 6 = 2p + 1

⇒p = 7

⇒2(7) + 1 = q

⇒14 + 1 = q

⇒15 = q

So, p = 7 and q = 15

Hence, the fraction is .

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