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 numbers are: 6a and 6b

ATQ,

6a + 6b = 60

a + b =10   .....(i)

⇒ LCM = HCF (a x b)

⇒ 150 = 6 (a x b)

⇒ ab = 25 .......(ii)

Now,

sum of their reciprocals = \(\frac{1}{6a}\) + \(\frac{1}{6b}\)

                                     = \(\frac{b + a}{6ab}\)

                                     = \(\frac{10}{150}\)                [from (i) & (ii)]

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