Question
The sum of two numbers is 99 and their HCF is 9. Total
number of such pairs of numbers is?  ÂSolution
According to question, HCF =9 Then, the two number will be 9a,9b Also, 9a+9b = 99, or , a+b =11 All possible pairs of positive integers a and b are (1,10),(2,9),(3,8),(4,7), and (5,6). Hence, required pairs of positive integers are = (9,90),(18,81),(27,72),(36,63), and (45,54). Hence, the number of pairs of positive integers is 5.
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