The sum of the ages of Ramesh and Mahesh is (2x² – 3x²y + y² + 3xy²) years. Age of Ramesh is (x² + 3x²y + y² + 3xy²) year. Find the age of Mahesh.

Correct option is A

Given:

The sum of the ages of Ramesh and Mahesh = $$2x^2 - 3x^2y + y^2 + 3xy^2$$​ years

The age of Ramesh  = $$x^2 + 3x^2y + y^2 + 3xy^2$$​ years

Solution:

Age of Mahesh = $$(2x^2 - 3x^2y + y^2 + 3xy^2) - (x^2 + 3x^2y + y^2 + 3xy^2)$$​​

​$$= 2x^2 - 3x^2y + y^2 + 3xy^2 - x^2 - 3x^2y - y^2 - 3xy^2$$​​

​$$= (2x^2 - x^2) + (-3x^2y - 3x^2y) + (y^2 - y^2) + (3xy^2 - 3xy^2)$$​​

​$$= x^2 - 6x^2y$$​​

Hence, the age of Mahesh is $$x^2 - 6x^2y$$​ years