Question

The arithemetic mean and geometric mean of two numbers are $14$ and $12$ respectively. What is the harmonic mean of the numbers?

• A. $10$
• B. $13$
• C. $\frac{32}{3}$
• D. $\frac{72}{7}$

Answer 1

The correct option is D $\frac{72}{7}$

Given, $a=14$ and $b=12$

Harmonic mean of $a$ and $b$ $=\frac{2ab}{a+b}$
$=\left(ab\right)\times \frac{1}{\left(\frac{a+b}{2}\right)}$
$=\frac{{\text{GM}}^2}{\text{AM}}=\frac{144}{14}=\frac{72}{7}$