Question

If $\frac{1}{a}+\frac{1}{b}=\frac{1}{c}$ and $ab=c.$ what is the average (arithmetic mean) of a and b?

• A. 0
• B. $\frac{1}{2}$
• C. 1
• D. $\frac{a+b}{2c}$

Answer 1

Answer: (B)

$\frac{1}{2}$

Given, $\frac{1}{a}+\frac{1}{b}=\frac{1}{c}$ and ab =c
Since, $\frac{1}{a}+\frac{1}{b}=\frac{1}{c}$
$\Rightarrow \frac{a+b}{ab}=\frac{1}{c}$
but given ab=c
$\Rightarrow \frac{a+b}{c}=\frac{1}{c}$
$\Rightarrow a+b=1$
Average of a and b is $\frac{a+b}{2}=\frac{1}{2}$
Option B is correct.