Question

The age of a man is three times the sum of the ages of his two sons. Five years hence, his age hi jiwill be double of the sum of the ages of his sons. Find the father's present age.

Answer 1

Let the sum of ages of two sons be x years Age of man = 3x years After 5 years age of the man = (3x + 5) years Sum of ages of two sons = (x + 10) years Given, (3x + 5) = 2(x + 10) ⇒ (3x + 5) = 2x + 20 ⇒ x = 15 Hence 3x = 3(15) = 45 Thus the age of the man(father) is 45 years.

Answer 2

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Present age of man is 45 years.

Given :-

The age of a man is three times the sum of the ages of his two sons.

5 years hence, his age will be double the sum of their ages.

To find :-

Present age of man.

Solution :-

Let ,

Man's present age = x years

Present age of 1st son = y years

Present age of 2nd son = z years

$\red{\underline{\sf{According\:to\:the\:1st\: condition:-}}}$

The age of a man is three times the sum of the ages of his two sons.

➪ x = 3(y+z)

➪ y+z = x/3 ..................(i)

$\red{\underline{\sf{According\:to\:the\:2nd\: condition:-}}}$

5 years hence, his age will be double the sum of their ages

5 years hence,

Man's age = (x+5) years

Age of 1st son = (y+5) years

Age of 2nd son = (z+5) years

➪ x+5 = 2[(y+5)+(z+5)]

➪ x+5 = 2(y+z+10)

[ put y+z = x/3 from eq (i)]

➪ x+5 = 2(x/3 + 10)

➪ x+5 = 2x/3 + 20

➪ x - 2x/3 = 20-5

➪ x/3 = 15

➪ x = 45

† Present age of man is 45 years.

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