Question

Appu’s mother is nine times as old as Appu. After nine years, her age would be three times that of Appu. What are their ages now?

Answer 1

Let Appu’s present age be x years

Appu’s mother’s present age = 9x years

After 9 years:

Appu’s age = (x + 9) years

Appu’s mother’s age = (9x + 9)

Algebraic form of the problem is:

9x + 9 = 3(x + 9)

⇒ 9x + 9 = 3x + 27

Subtracting 3x from both the sides:

⇒ 9x + 9 − 3x = 3x + 27 − 3x

⇒ 6x + 9 = 27

Subtracting 9 from both the sides:

⇒ 6x + 9 − 9 = 27 − 9

⇒ 6x = 18

Dividing both the sides by 6:

Therefore, Appu’s present age is 3 years and her mother’s present age is 27 (= 9 × 3) years.