Question

Rohan's mother is $26$ years older than him. The product of their ages $3$ years from now will be $360$. Formulate the quadratic equation to find their ages and find the mother's present age.

Answer 1

Let Rohan present age be $x$ years. Then, his mother's age is $(x+26)$ years.

Rohan's age after 3 years $=(x+3)$ years

After 3 years the age of Rohan's mother$=(x+26+3)$years$=(x+29)$ years

It is given that after 3 years from now, the product of Rohan's and his mother's ages will be $360$ years

$\therefore (x+3)(x+29)=360\Rightarrow x^2+32x-273=0$....answer

This is the required equation.

$\therefore (x+39)(x-7)=0$

$\therefore x=-39$ and $x=7$

$\therefore x=7$.......($\because$ $x$ can not be negative)

$\therefore$ Mother's present age$=7+26=33$....answer