If sum of two numbers is 1215 and their HCF is 81, then the possible number of pairs of such numbers are

(a) 2   (b) 3   (c) 4   (d) 5

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Transcript

Question 21 If sum of two numbers is 1215 and their HCF is 81, then the possible number of pairs of such numbers are (a) 2 (b) 3 (c) 4 (d) 5 Since HCF of both numbers is 81 It means 81 is a factor of both numbers Thus, let us assume numbers are 81x and 81y Where x and y are co-prime numbers Now, given that Sum of numbers = 1215 81x + 81y = 1215 81(x + y) = 1215 (x + y) = 1215/81 x + y = 15 Here, x and y are co-prime numbers So, Possible values of x and y can be 1 and 14 2 and 13 4 and 11 7 and 8 Thus, there are 4 such pairs So, the correct answer is (c)

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.