The difference between the two numbers is 15 and their HCF and LCM are 3 and 108 respectively. Find the difference between their inverses?
Answer & explanation
Correct answer: option 2
⇒ (Product of two other factors) × HCF = LCM
⇒ (a × b) × 3 = 108
⇒ (a × b) = 36
So a and b = 9 and 4
Therefore, numbers are:
= (a × HCF), (b × HCF)
= (9 × 3), (4 × 3) = 27 , 12
ATQ,
Difference = 27 - 12 = 15 (given)
So, Difference of their reciprocal is
⇒ \(\frac{1}{12}\) - \(\frac{1}{27}\) = \(\frac{9\;-\;4}{108}\) = \(\frac{5}{108}\)