Number pairs given sum and HCF

Let the two numbers be $9x$ and $9y$, where $x$ and $y$ are co-prime natural numbers.

$9x + 9y = 135 \Rightarrow x + y = 15$.

Co-prime pairs $(x, y)$ that sum to 15 are $(1, 14), (2, 13), (4, 11), (7, 8)$.

Thus, 4 such pairs can be formed.