Correct option is (C) 12
Let the age of mother be x years and
age of her son be y years.
12 years ago, the mother age was (x - 12) years
14 years ago, the mother age was (x - 14) years
9 years hence, the mother's age will be (x+9) years
and her son's age will be (y+9) years
According to given conditions, we have
x+y = 2 (x - 12)
\(\Rightarrow\) x+y = 2x - 24
\(\Rightarrow\) y = x - 24 ______________(1)
And (x+9) + (y+9) = 3 (x - 14)
\(\Rightarrow\) x + y + 18 = 3x - 42
\(\Rightarrow\) x + x - 24 + 18 = 3x - 42
\(\Rightarrow\) 2x - 6 = 3x - 42
\(\Rightarrow\) 2x - 3x = 6 - 42
\(\Rightarrow\) -x = -36
\(\Rightarrow\) x = 36
\(\therefore\) y = 36 - 24 = 12 (From (1))
Hence, her son’s present age is 12 years.
