​If the ratio of two numbers is 5 : 3 and the product of their LCM and their HCF is 135, then the sum of the reciprocals of the LCM and the HCF is:​​​

Correct option is A

Given:

The ratio of the two numbers is 5 : 3

The product of their LCM and HCF is 135

Formula Used:

LCM × HCF = Product of the numbers

Solution:

Let the two numbers be 5x and 3x

The product of the numbers: 

(5x) × (3x) = 135

15x² = 135

x= $$\frac{135}{15}$$​ = 3

The two numbers are 5x = 15 and 3x = 9

The HCF of 15 and 9 is 3, and the LCM of 15 and 9 is 45

The sum of the reciprocals of the LCM and HCF:

= $$\frac{1}{\text{LCM}} + \frac{1}{\text{HCF}}$$​​

​$$= \frac{1}{45} + \frac{1}{3}$$​​

​$$= \frac{1}{45} + \frac{15}{45}$$​​

​$$= \frac{16}{45}$$​​

Thus, the sum of the reciprocals of the LCM and HCF = $$\frac{16}{45}$$​​