# A father&rs

Let, the present age of the father is x and the age of two children be xand 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 + 5 = 2(x1 + x2 + 10)
⇒ x + 5 = 2(x1 + x2 ) + 20

⇒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)

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

Put the value of p in (2) to get,
⇒2(7) + 1 = q
⇒14 + 1 = q
⇒15 = q

So, p = 7 and q = 15

Hence, the fraction is .

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