Question

The sum of two numbers is $20$, their product is $40$. The sum of their reciprocals is

• A. $\frac{1}{10}$
• B. $4$
• C. $2$
• D. $\frac{1}{2}$

Answer 1

The correct option is D $\frac{1}{2}$

Let the numbers are $x$ and $y$.
From question, we have

$x+y=20$ and $xy=40$
Sum of the reciprocal of the numbers $x$ and $y$
$\frac{1}{x}+\frac{1}{y}=\frac{y+x}{xy}=\frac{20}{40}=\frac{1}{2}$