Question

six years ago, the age of mother was equal to the square of her son's age. three years hence, her age will be thrice the age of her son then. find the present ages of the mother. and son.

Answer 1

Answer:

Son = 12 years

Mother = 42 years 

Explanation - 

Six years ago let the son age = x

Mother = x² 

Present ages now:

Son = x + 6

Mother = x²  + 6

3 years later:

Son = x + 6 + 3 = x + 9

Mother =  x²  + 6 + 3 =  x²  + 9

Solving x - 

x²  + 9 = 3(x + 9)

x²  + 9 = 3x + 27

x²  - 3x - 18 = 0

(x - 6)(x + 3) = 0

x = 6 or x = -3

Take x = 6. As the other value is (- value)

Finding their Present age -

Son = x + 6 = 6 + 6 = 12 years.

Mother =  x²  + 6 = (6)² + 6 = 42 years.

Hence : 

Son = 12 years

Mother = 42 years