Correct Answer - Option 3 : 51/650
Given:
HCF = 5
LCM = 130
The sum of the two numbers = 51
Concept Used:
The product of two numbers = HCF × LCM
Calculation:
Let the two numbers be A and B
According to the question, we have
The sum of the two numbers = A + B
⇒ A + B = 51
and the product of two numbers = HCF × LCM
A × B = 5 × 130
⇒ AB = 650
Now, the sum of reciprocals of two numbers is
(1/A) + (1/B) = (A + B)/AB
⇒ 51/650
∴ The reciprocals of the two numbers are (51/650).