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Assume two numbers are a,b.
Given: HCF(a,b) =5
LCM(a,b) = 120
ATQ
a + b = 55...(i)
We know HCF x LCM = axb
5x 120 = a x b
a x b = 600...(ii)
Put value of a and b is equation (i)
600/b + 600/a = 55
(1/a + 1/b) = 55/600 = 11/120
Hence the sum of the reciprocals of the numbers is 11/120.