Question : The sum of the two numbers is 18 and their HCF and LCM are 3 and 54, respectively. What will be the sum of their reciprocals?
Option 1: $\frac{1}{7}$
Option 2: $\frac{1}{11}$
Option 3: $\frac{1}{6}$
Option 4: $\frac{1}{9}$
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Correct Answer: $\frac{1}{9}$
Solution : Let the two numbers be $x$ and $y$. We know (HCF) × (LCM) = Product of two numbers Given HCF = 3 and LCM = 54 ⇒ $x × y = 3 × 54$ Also, $x + y = 18$ Now to calculate, $\frac{1}{x} + \frac{1}{y}$ = $\frac{x + y}{xy}$ = $\frac{18}{3 × 54} = \frac{1}{9}$ Hence, the correct answer is $\frac{1}{9}$.
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