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1. 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:

A. $\frac{55}{601}$

B. $\frac{601}{55}$

C. $\frac{11}{120}$

D. $\frac{120}{11}$

Solution:

\begin{aligned} Let the numbers be a and b \\ Then, a + b = 55 and \\ a b = 5 \times 120 = 600 \\ ∴ The required sum \\ = \frac{1}{a} + \frac{1}{b} = \frac{a + b}{a b} = \frac{55}{600} = \frac{11}{120} \end{aligned}

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