Question

The prodcut of Shikha's age five years ago and her age 8 years later is 30, her age at both times being given in years. Find her present age.

Answer 1

Let the present age of Shikha be x years.
According to the question,

⇒ $(x–5)(x+8)=30$

⇒ $x^2+8x–5x–40=30$

⇒ $x^2+3x=30+40$

⇒ $x^2+3x=70$

⇒ $x^2+3x–70=0$

⇒ $x^2+10x–7x–70=0$

⇒ $x(x+10)-7(x+10)=0$

⇒ $(x-7)(x+10)=0$

⇒ $x=7orx=-10$

We need to discard the value of x = -10, as age cannot be negative.
So, the present age of Shikha is 7 years.