Question

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

• A. $0$
• B. $1$
• C. $\frac{1}{2}$
• D. $2$

Answer 1

The correct option is C

$\frac{1}{2}$

Explanation for the correct answer:

$\frac{1}{\mathrm{a}}+\frac{1}{\mathrm{b}}=\frac{1}{\mathrm{c}}$

$\Rightarrow$ $\frac{\mathrm{b}+\mathrm{a}}{\mathrm{ab}}=\frac{1}{\mathrm{c}}$

$\Rightarrow$ $\mathrm{b}+\mathrm{a}=\frac{\mathrm{ab}}{\mathrm{c}}$

$\Rightarrow$ $\mathrm{b}+\mathrm{a}=1$ $...\left(\because \mathrm{ab}=\mathrm{c}\right)$

Arithmetic mean of $\mathrm{a}$ and $\mathrm{b}$ $=\frac{\mathrm{a}+\mathrm{b}}{2}=\frac{1}{2}$

Hence, the required arithmetic mean is $\frac{1}{2}$, so, option $\left(\mathrm{C}\right)$ is the correct answer.