Question

The sum of two numbers is 60 and their HCF and LCM are 12 and 72 respectively. The sum of the reciprocal of the two numbers is:
1. \(\frac{5}{12}\)
2. \(\frac{1}{5}\)
3. \(\frac{5}{72}\)
4. \(\frac{5}{6}\)

Answer 1

Correct Answer - Option 3 : \(\frac{5}{72}\)

Given:

Sum of the numbers = 60

HCF = 12

LCM = 72

Formula used:

Product of two numbers = HCF × LCM

Calculation:

Let the numbers be a and b.

Product of two numbers = HCF × LCM

⇒ ab = 12 × 72

The sum of two numbers is 60

⇒ a + b = 60

According to the question,

Sum of reciprocal of the number = 1/a + 1/b

⇒ (a + b)/ab

⇒ 60/(12 × 72)

⇒ 5/72

∴ The sum of reciprocal of a and b = 5/72.