Question

Age of a father is 3 times the sum of ages of his two sons. 5 years hence age of father will be two times the sum of ages of his two sons find present age of father.
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Answer 1

Given :

• Age of a father is 3 times the sum of ages of his two sons.
• 5 years hence age of father will be two times the sum of ages of his two sons.

To find :

• Present age of father.

Solution :

Consider,

• Age of father = x years.
• Age of 1st son = y years.
• Age of 2nd son = z years.

According to the 1st condition :-

• Age of a father is 3 times the sum of ages of his two sons.

$\to\sf{x=3(y+z)}$

$\to\sf{x=3y+3z..............eq[1]}$

According to the 2nd condition :-

• 5 years hence age of father will be two times the sum of ages of his two sons.

After 5 years,

• Age of father = (x+5) years
• Age of 1st son = (y+5) years
• Age of 2nd son = (z+5) years

$\to\sf{x+5=2[(y+5)+(z+5)]}$

$\to\sf{x+5=2(y+z+10)}$

$\to\sf{3y+3z+5=2y+2z+20\:[put\:x=3y+3z\: from\:eq(1)]}$

$\to\sf{y+z=15}$

• Now put y+z = 20 in eq[1].

$\to\sf{x=3(y+z)}$

$\to\sf{x=3\times\:15}$

$\to\sf{x=45}$

Therefore, the present age of father is 45 years.

Answer 2

$\huge\sf\underline{\pink{An}\purple{sW}\green{eR}}$

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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