Correct Answer: 135

Solution : The factor of 36x ² – 81y ² = 9 × (4x ² - 9y ² )
The factor of 81x ² – 9y ² = 9 × (9x ² - y ² )
So, the HCF of (36x ² – 81y ² ) and (81x ² – 9y ² ) is 9 as 9 is the only highest and most common factor of the given equation.
But it is also given that the highest common factor (HCF) of x and y is 15 which means one more factor is 15.
On multiplying 15 with 9, the HCF of 36x ² – 81y ² and 81x ² – 9y ² is determined which is divisible by itself as well.
⇒ 15 × 9 = 135
Hence, the correct answer is 135.