# A mother said to her son “The sum of our present ages is twice my age 12 years ago and 9 years hence,

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A mother said to her son “The sum of our present ages is twice my age 12 years ago and 9 years hence, the sum of our ages will be thrice my age 14 years ago”. What is her son’s present age ? (in years)

A) 18

B) 14

C) 12

D) 10

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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.

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Correct option is C) 12