The sum of two numbers is 528 and their HCF is 33. The number of pairs of numbers satisfying the above conditions is = ?

Explanation:-

Let the required numbers be 33a and 33b.
Then 33a + 33b = 528
⇒ a + b = 16
Now co - primes with sum 16 are (1, 15), (3, 13), (5, 11) and (7, 9)
∴ Required numbers are (33 × 1, 33 × 15), (33 × 3, 33 × 13), (33 × 5, 33 × 11), (33 × 7, 33 × 9)
The number of such pairs is 4.