The sum of two non co ndash prime numbers added to their HCF gives us 91 How many such pairs are pos...........

Explanation:

Let HCF of the numbers be h.
The numbers can be taken as ha + hb, where a, b are coprime.
h + ha + hb = 91
h(1 + a + b) = 91
h ≠ 1
h = 7
=> 1 + a + b = 13 a + b = 12
h = 13
=> 1 + a + b = 7
=> a + b = 6
Case 1: h = 7, a + b = 12
(1, 11), (5, 7) => Only 2 pairs are possible as a, b have to be coprime.
Case 2: h = 13, a + b = 6
(1, 5) only one pair is possible as a, b have to be coprime.
Overall, 3 pairs of numbers are possible – (7, 77) (35, 49) and (13, 65)