NCHMCT JEE 2013 Question Paper with solutions for online practice

Let the present ages of father and son be x years and (45 – x) years
then, (x – 5)(45 – x – 5) = 4(x – 5)
⇒ (x – 5)(40 – x) = 4x – 20
⇒ 40x – ${\mathit{x}}^2$ – 200 + 5x = 4x – 20
⇒ 45x – ${\mathit{x}}^2$ – 200 = 4x – 20
⇒ ${\mathit{x}}^2$ – 45x + 4x + 200 – 20 = 0
⇒ ${\mathit{x}}^2$ – 41x + 180 = 0
⇒ ${\mathit{x}}^2$ – 36x – 5x + 180 = 0
⇒ x(x – 36) – 5(x – 36) = 0
⇒ (x – 5)(x – 36) = 0
x = 5, 36
∴ Present ages of father and son be 36 years and 9 years.