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

Solution:

Let the numbers be x and y
Then,
x + y = 40 and xy = 375

\begin{aligned} ∴ \frac{1}{x} + \frac{1}{y} = \frac{x + y}{x y} \\ = \frac{40}{275} \\ = \frac{8}{75} \end{aligned}

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