**Solution:**

Let the required numbers be 9a and 9b

Then, 9a + 9b = 135

⇒ a + b = 15

Now, co-primes with sum 15 are

(1, 14), (2, 13), (4, 11), (7, 8)

∴ Required numbers are (9 × 1, 9 × 14), (9 × 2, 9 × 13), (9 × 4, 9 × 11) and (9 × 7, 9 × 8)

i.e., (9, 126), (18, 117), (36, 99) and (63, 72)

Hence, the number of such pairs is 4.

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