SSC Selection Post 2022 PYQ — Question 51

The correct answer is option 4 i.e. 27.

$64y^3 = (4y)^3$

$x^3 + (4y)^3 + 36xy$

$x^3 + (4y)^3 = (x + 4y)^3 - 3x \times 4y (x + 4y) = (x + 4y)^3 - 12xy(x + 4y)$

Now adding 36xy :

$x^3 + 64y^3 + 36xy = (x + 4y)^3 - 12xy(x + 4y) + 36xy$

Substitute x = 3 - 4y : x + 4y = 3

$xy = (3 - 4y)y = 3y - 4y^2$

$(3)^3 - 12(3y - 4y^2)(3) + 36(3y - 4y^2) \$

$= 27 - 36(3y - 4y^2) + 108y - 144y^2 = 27 - 108y + 144y^2 + 108y - 144y^2 = 27$