Question
If the sum of the number is 91 and their HCF and LCM are
7 and 280 respectively. Find the sum of their reciprocals?Solution
HCF = 7 and LCM = 280 (given) Sum of the number = 91 Let the first number be x and the second number be y. Now, x+y = 91 ............... (i) Again, first number × second number = HCF × LCM or xy = 7 × 280 = 1960 ........ (ii) Solving (i) and (ii) we got, x = 56, y = 35 ∴ Sum of reciprocals = 1/56 + 1/35 = (5+8)/280 = 13/280
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