Question

The ages of Kavya and Karthik are 11 years and 14 years. In how many years time will the product of their ages be 304?

Answer 1

It is given that the present age of Kavya is $11$ years, then her age after $x$ years is $(11+x)$ years.

Also, the present age of Karthik is $14$ years, then his age after $x$ years is $(14+x)$ years.

It is also given that the product of their ages after $x$ years is $304$, therefore,

$(11+x)(14+x)=304\Rightarrow 154+11x+14x+x^2=304\Rightarrow x^2+25x+154-304=0\Rightarrow x^2+25x-150=0\Rightarrow x^2+30x-5x-150=0\Rightarrow x(x+30)-5(x+30)=0\Rightarrow (x-5)=0,(x+30)=0\Rightarrow x=5,x=-30$

Since the age of a person cannot be negative thus, $x=5$.

Hence, after $5$ years the product of their ages will be $304$.