Correct Answer  Option 2 : x ≥ y
According to given equations
I. x2 – 27x + 162 = 0
⇒ x2 – 18x – 9x + 162 = 0
⇒ x(x – 18) – 9(x – 18) = 0
⇒ (x – 18) (x – 9) = 0
⇒ x = 18, 9
II. y2 + 6y – 135 = 0
⇒ y2 + 15y – 9y – 135 = 0
⇒ y(y + 15) – 9(y + 15) = 0
⇒ (y + 15) (y – 9) = 0
⇒ y = 9, 15
Comparison between x and y (via Tabulation):
x

y

Relation

18

9 
x>y 
18 
15

x>y

9

9

x=y

9

15

x>y

∴ x ≥ y