The sum of two numbers is 55 and the HCF and LCM of these two numbers are 5 and 20 respectively. Find the sum of reciprocals of these numbers.

When the product of two numbers is 1, they are said to be reciprocals of each other.

Answer: The sum of the reciprocals of two numbers whose sum is 55 and the HCF and LCM are 5 and 20 respectively is 11/20.

Let's find the sum of reciprocals of the given numbers.

Explanation:

Let the two numbers be 'x' and 'y'.

According to the question,

Sum of the numbers = 55

Thus, x + y = 55 --------------------------------- (1)

HCF of the numbers = 5

LCM of the numbers = 20

We know that,

HCF × LCM = Product of the numbers

⇒ xy = HCF × LCM

⇒ xy = 5 × 20

⇒ xy = 100 ------------------------------ (2)

Sum of their reciprocals will be:

(1/x) + (1/y) = (y + x) / xy (on taking LCM)

Thus, we will evaluate (y + x) / xy 

On substituting the values from equation (1) and (2) we get,

55 / 100 = 11 / 20

Thus, the sum of the reciprocals of two numbers whose sum is 55 and the HCF and LCM are 5 and 20 respectively is 11/20.