Question

Kailash's age at present is $2$ years less than $6$ times the age of his daughter Prerna. The product of their ages $5$ years later will be $330$. What was the age of Kailash when his daughter Prerna was born?

Answer 1

Let the present age of Prerna $=x$ years
According to the given condition
Age of her Kailash $=(6x-2)$ years
After $5$ years
Age of Prerna$=(x+5)$ years
Age of Kailash $=\left[\right(6x-2)+5]=(6x+3)$ years
Product of their ages after $5$ years is $330$
$(x+5)(6x+3)=330$
$\therefore$ $6x^2+33x+15=330$
$\therefore$ $6x^2+33x-315=0$
$\therefore$ $2x^2+11x-105=0$
$\therefore$ $2x^2+21x-10x-105=0$
$\therefore$ $(2x+21)(x-5)=0$
$\therefore$ $x=-\frac{21}{2}$ OR $x=5$
$\therefore$ $x=5$ (age cannot be negative)
Thus, present age of Prerna $=5$ years
Present age of Kailash $=x-2=28$ years
Then, Age of Kailash when Prerna was born will be $5$ years less than his present age $=23$ years