Question

Rohan's mother is $26$ years older than him. The product of their ages (in years) $3$ years from now will be $360$. Find Rohan's present age.

• A. $12$ years
• B. $6$ years
• C. $10$ years
• D. $7$ years

Answer 1

The correct option is D $7$ years

Let the present age Rohan be $x$.
Hence his mother's present age is $(x+26)$ years.
Three years form now, their ages will be $(x+3)$ and $(x+29)$
Now,
$(x+3)(x+29)=360$
$x^2+32x+87=360$
$x^2+32x-273=0$
$(x-7)(x+39)=0$
Hence $x=7$ and $x=-39$
Since, negative value of $x$ is not possible,

Hence, present age of Rohan is $7$, years.