Question

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

Answer 1

Let the age of Rohan be “ x ”
Then Age of Rohan's mother = x+26

After three years their ages are (x+3),(x+29) respectively .

According to the question ;

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

x²+(3+29)x+87=360

x²+32x-273=0

x²+39x-7x-273=0

x(x+39)-7(x+39)=0

(x+39)(x-7)=0

x = 7 or -39

As Age can never be negative we have x =7.

Therefore ,Present age of Rohan =7 years.

Answer 2

Let Rohan's age be x
Then his mother's age is x+26

After 3 years,
Rohan's age = x + 3
His mother's age = x + 26 + 3 = x + 29

Product of their ages after 3 years = 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
x(x+39) - 7(x+39) = 0
(x+39) (x-7) = 0

x+39 = 0
=> x = -39 ✖ age can't be negative

x-7 = 0
=> x = 7 ✔

Rohan's present age = 7
his mother's age = 7+26 = 33

Hope it helps