Question

The present age of the mother is square of her daughter's present age. 4 years hence, she will be 4 times as old as her daughter. Find their present ages.

Answer 1

Let the present age of the Mother be M years and her daughter age be D years. 

Then, as per the question description, 

M = D² ...... (i) 

(M + 4) = 4(D + 4) ...... (ii) 

Putting (ii) in (i) above, we get 

D² + 4 = 4D +16 

⇒ D² - 4D -12 = 0 

⇒ D² - 6D + 2D - 12 = 0 

⇒ D(D-6 )+ 2(D-6)=0 

⇒ (D+ 2)(D-6)=0 

⇒ D= -2, D = 6  (Age cannot be negative) 

⇒ D =6 years and hence, M =36 years