# If the sum of two numbers is 55 and the H.C.F. and L.C.M. of these numbers are 5 and 120 respectively, then the sum of the reciprocals of the numbers is equal to:

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.

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