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: $\frac{1}{9}$

Question

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: $\frac{1}{9}$

Team Careers360 · Accepted Answer

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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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: 17Option 2: 111Option 3: 16Option 4: 19

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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: $\frac{1}{9}$