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# Discussion

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.$$\dfrac{55}{601}$$
• B.$$\dfrac{601}{55}$$
• C.$$\dfrac{11}{120}$$
• D.$$\dfrac{120}{11}$$

Let the numbers be $$a$$ and $$b$$.
Then,
$$a + b = 55$$ and
$$ab = 5 \times 120 = 600$$
The required sum
$$=\dfrac{1}{a} + \dfrac{1}{b}\\~\\= \dfrac{a+b}{ab}\\~\\=\dfrac{55}{600}\\~\\= \dfrac{11}{120}$$

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