The sum of two numbers is 40 and their product is 375. What will be the sum of their reciprocals ?

A. $$\frac{1}{40}$$

B. $$\frac{8}{75}$$

C. $$\frac{75}{4}$$

D. $$\frac{75}{8}$$

Answer: Option B

Solution(By Examveda Team)

Let the numbers be x and y
Then,
x + y = 40 and xy = 375
$$\eqalign{ & \therefore \frac{1}{x} + \frac{1}{y} = \frac{{x + y}}{{xy}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{{40}}{{275}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{8}{{75}} \cr} $$