If the sum of two numbers is 60 and the HCF and LCM of these numbers are 6 and 150 , then the sum of their reciprocals is-

\(\frac{1}{15}\)

Let the two numbers be $a$ and $b$.

Given:

• $a + b = 60$
• HCF $= 6$
• LCM $= 150$

We know:

$ab = \text{HCF} \times \text{LCM} = 6 \times 150 = 900$

The sum of their reciprocals is:

$\frac{1}{a} + \frac{1}{b} = \frac{a + b}{ab} = \frac{60}{900} = \frac{1}{15}$