Question

A man is four times as old as his son after 12 years he will be twice as old as his son find the age of his son

Answer 1

SOLUTION :-

Let,

Age of son = x

Age of man = y

After 12 years,

Age of son = x + 12

Age of man = y + 12

According to the first condition,

$\longrightarrow\sf y = 4x \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ................(1)$

According to the second condition,

$\longrightarrow\sf 2(x+12)=y+12 \\\\\longrightarrow 2x+24= y+12 \\\\\longrightarrow 2x-y = -12 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ................(2)$

Substitute the value of y in eq(2),

$\longrightarrow\sf 2x - 4x = -12 \\\\\longrightarrow -2x = -12 \\\\\longrightarrow\bf x = 6$

Age of son = 6 years

Age of man = 4 × 6 = 24 years

Answer 2

Answer :-

• Age of his son is 6 years.

Given :-

• A man is four times as old as his son. After 12 years he will be twice as old as his son.

To Find :-

• Age of his son.

Solution :-

Let

• The age of son be x
• Man's present age will be 4x

After 12 years :-

• Son's age will be x + 12
• Man's age wil be 4x + 12
• Man's age is twice as old as his son.

According to question :-

2 (x + 12) = 4x + 12

2x + 24 = 4x + 12

4x - 2x = 24 - 12

2x = 12

x = 12/2

x = 6

Hence, the age of his son is 6 years.