Question

Rohan’s mother is 26 years older than him. The product of their ages after 3 years will
be 360 years. We need to find Rohan’s present age

Answer 1

Let, Rohan's present age be x years.

So, according to the question, we can say that her mother's age would be (x + 26) years

After 3 years, Rohan's age = x + 3

Her mother's age would be = x + 26 + 3 = x + 29 years.

Given, their product is 360

→ (x + 3)(x + 29) = 360

→ x² + 29x + 3x + 87 = 360

→ x² + 32x + 87 - 360 = 0

→ x² + 32x - 273 = 0

→ x² + 39x - 7x - 273 = 0

(By splitting the middle terms)

→ x(x + 39) - 7(x + 39) = 0

→ (x - 7)(x + 39) = 0

→ (x - 7) = 0/(x + 39)

→ x - 7 = 0

→ x = 7

Similarly, x = -39

But, age cannot be negative, hence x = 7 years.

So, present age of Rohan is 7 years.

Answer 2

$\bf\huge\textbf{\underline{\underline{According\:to\:the\:Question}}}$  

Suppose the age of Rohan be p

And Mother age be p + 26

According to given condition

(p + 3)(p + 26 + 3) = 360

(p + 3)(p + 29) = 360 [Factorize in meaningful]

p^2 + 29p + 3p + 87 = 360

p^2 + 32p = 360 - 87

p^2 + 32p - 273 = 0

$\bf\huge{\implies p = \dfrac{-b+\sqrt{b^2 - 4ac}}{2a}}$        

$\bf\huge{\implies p = \dfrac{-32+\sqrt{1024 + 1092}}{2}}$    

$\bf\huge{\implies p = \dfrac{-32+46}{2}}$  

$\bf\huge{\implies p = \dfrac{-32+46}{2}}$  

$\bf\huge{\implies p = \dfrac{14}{2}}$  

p = 7

Hence

$\bf\huge\bf\huge{\boxed{\bigstar{{Rohan \:age = 7\:years}}}}$

Mother age

= 7 + 26

$\bf\huge\bf\huge{\boxed{\bigstar{{Mother\:age=33 \:years}}}}$