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1. If the sum of two numbers is 36 and their HCF and LCM are 3 and 105 respectively, the sum of the reciprocals of the numbers is = ?

A. $\frac{2}{35}$

B. $\frac{3}{35}$

C. $\frac{4}{35}$

D. None of these

Solution:

Let the number be a and b

\begin{aligned} Then, \\ a + b = 36 and \\ a b = 3 \times 105 = 315 \\ ∴ Required sum \\ = \frac{1}{a} + \frac{1}{b} \\ = \frac{a + b}{a b} \\ = \frac{36}{315} \\ = \frac{4}{35} \end{aligned}

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