Question

2. The age of father is 20 years more than twice the age of the son. If sum of their ages is
65 years, find the age of the son and the father. -
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Answer 1

Given :

• The sum of their ages is 65 years.
• The age of father is 20 years more than twice the age of the son.

To find :

• Present age of father and son.

Solution :

Consider,

• Present age of father = x years
• Present age of son = y years

According to the 1st condition :-

• The sum of their present ages is 65 years.

$\to\sf{x+y=65}$

$\to\sf{x=65-y.................(1)}$

According to the 2nd condition :-

• The age of father is 20 years more than twice the age of the son.

$\to\sf{x=2y+20}$

$\to\sf{65-y=2y+20\:[put\:x=65-y\: from\: eq (1)}$

$\to\sf{-y-2y=20-65}$

$\to\sf{-3y=-45}$

$\to\sf{y=15}$

• Present age of son = 15 years

Now, put y = 15 in eq(1) for getting the value of x.

$\to\sf{x=65-y}$

$\to\sf{x=65-15}$

$\to\sf{x=50}$

• Present age of father = 50 years

Therefore , the present age of father is 50 years & the present age of son is 15 years.

Answer 2

Answer:

Let the Age of Son be n years.

☆ Age of Father :

⇏ Father = 20 yrs more than Twice of Son

⇏ Father = 20 + 2 × n

⇏ Father = 20 + 2n

━━━━━━━━━━━━━━━━━━━

☢ According to the Question :

⇢ Sum of Ages = 65 years

⇢ Son + Father = 65 years

⇢ n + (20 + 2n) = 65

⇢ n + 20 + 2n = 65

⇢ 3n = 65 - 20

⇢ 3n = 45

• Dividing both term by 3

⇢ n = 15 years ⠀⠀⠀⠀[ Age of Son ]

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☢ Required Ages of Both :

• Son = n = 15 years

• Father = (20 + 2n) = 50 years