Question

Question 2(iii)
Represent the following situations in the form of quadratic equations.
(iii) Rohan's mother is 26 years older than him. The product of their ages (in years) 3 years from now will be 360. We would like to find Rohan's present age.

Answer 1

(iii) Let take Rohan's age = $xyears$
Hence, his mother's age = $x+26$
$3$ years from now
Rohan's age = $x+3$
Age of Rohan's mother will =$x+26+3=x+29$
The product of their ages $3$ years from now will be $360$ so that
$(x+3)(x+29)=360$
$\Rightarrow x^2+29x+3x+87=360\Rightarrow x^2+32x+87-360=0$
$\Rightarrow x^2+32x-273=0$
$\Rightarrow x^2+39x-7x-273=0$
$\Rightarrow x(x+39)-7(x+39)=0$
$\Rightarrow (x+39)(x-7)=0$
Either $x+39=0orx-7=0$
$\Rightarrow x=-39orx=7$
As, age cannot be in negative value
hence, $x=7$,Rohan's age = $7years$
his mother's age = $7+26=33years$