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The sum of the two numbers is 51 and their HCF and LCM are 5 and 130 respectively. Find the sum of reciprocals two numbers.
1. 53/625
2. 57/650
3. 51/650
4. 59/525

1 Answer

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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).

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