The sum of two numbers is 18 and their HCF and LCM are 3 and 54 respectively. What will be the sum of their reciprocals?
Answer & explanation
Correct answer: option 4
H.C.F. = 3
L.C.M. = 34
Sum of two numbers = 18
Let the two numbers be x and y.
⇒ x + y = 18
Also, xy = 3 × 54 = 162
Sum of reciprocal of these numbers,
\(\frac{1}{x} + \frac{1}{y}\) = \(\frac{x + y}{xy}\)
\(\frac{x + y}{xy}\) = \(\frac{18}{162}\) = \(\frac{1}{9}\)