The number of pairs of positive integers whose sum is 99 and HCF is 9 is

Correct option is B

Given:
Sum of integers = 99
Highest Common Factor (HCF) = 9
Formula Used:
Let the numbers be HCF × a and HCF × b, where a and b are co-prime integers.
Solution:
Let the two positive integers be 9a and 9b.
9a + 9b = 99
Divide the entire equation by 9.
a + b = 11
We need to find pairs of (a, b) such that a and b are positive, co-prime, and sum up to 11.
The possible pairs are:
(1, 10)
(2, 9)
(3, 8)
(4, 7)
(5, 6)
Since all these pairs are co-prime, there are 5 valid pairs.
Final Answer
So the correct answer is (b)