Question

Six years before the age of mother was equal to the square of her son age three year hence,her age will be thrice the age of her son then find the present ages of the mother and son

Answer 1

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Answer 2

Given :

Six years before the age of the mother was equal to the square of her son age three years hence, her age will be thrice the age of her son.

To find :

The present ages of the mother and son

Solution :

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 : 

The present age of Son = 12 years

The present age of the Mother = 42 years