Question

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

• A. 39
• B. 7
• C. 14
• D. 10

Answer 1

The correct option is B

7

Let's 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 $360$.

$(x+3)(x+29)=360$

$\Rightarrow x^2+29x+3x+87=360$

$\Rightarrow x^2+32x+87-360=0$

$\Rightarrow x^2+32x-273=0$

$\Rightarrow x^2+2\times x\times 16+256=273+256$

$\Rightarrow (x+16{)}^2=529$

$\Rightarrow x+16=\pm 23$

$\Rightarrow x=-39orx=7$

As age cannot be in negative value,

Rohan's age = $7years$

Mother's age = $7+26=33years$