The sum of two positive integers is 55. If their HCF and LCM are 5 and 120, respectively, then the sum of their reciprocals is________.

Correct option is B

Given:

Sum of two integers = 55
HCF = 5, LCM = 120

Formula Used:

For two numbers, product = HCF × LCM
Sum of reciprocals = $$\frac{1}a + \frac{1}{b} = \frac{a + b}{a × b}$$​​

Solution:

From the product formula:
a × b = HCF × LCM = 5 × 120 = 600 

Sum of integer;

a + b = 55
Sum of reciprocals = $$\frac{a + b}{a × b}$$​ = $$\frac{ 55 }{ 600}$$​ = $$\frac{11}{ 120}$$​​

Sum of reciprocals = $$\frac{11}{ 120}$$​​