A mother said to her son “The sum of our present ages is twice my ag

1.	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
Answer» 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. Correct option is C) 12

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

Answer»

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.

Correct option is C) 12