If the sum of two numbers is 36 and their HCF and LCM are 3 and 105 respectively, the sum of the reciprocals of the numbers is = ?

A. $$\frac{2}{{35}}$$

B. $$\frac{3}{{35}}$$

C. $$\frac{4}{{35}}$$

D. None of these

Answer: Option C

Solution(By Examveda Team)

Let the number be a and b
$$\eqalign{ & {\text{Then,}} \cr & a + b = 36\ \text{and} \cr & ab = 3 \times 105 = 315 \cr & \therefore {\text{Required sum}} \cr & {\text{ = }}\frac{1}{a} + \frac{1}{b} \cr & = \frac{{a + b}}{{ab}} \cr & = \frac{{36}}{{315}} \cr & = \frac{4}{{35}} \cr} $$