Question

The age of the mother is 2 times the age of her daughter. 8 years hence the age of mother will be 4 years more than 3 times the age of her daughter. find their age

Answer 1

Let the present age of the son be x yearsHence the present age of man = 2x2 yearsAge of son after 8 years = (x + 8) yearsAge of man after 8 years = (2x2 + 8) yearsGiven that (2x2 + 8) = 3(x + 8) + 4 ⇒  (2x2+ 8) = 3x + 24 + 4 ⇒ 2x2 – 3x – 20 = 0 ⇒ 2x2 – 8x + 5x – 20 = 0 ⇒ 2x(x – 4) + 5(x – 4) = 0 ⇒ (x – 4)(2x + 5) = 0 ⇒ (x – 4) = 0 or (2x + 5) = 0 ∴ x = 4 or x = – 5/2 Thus x = 4 Hence present age of son is 4 years and present age of man is 32 years.