Question

If $H$ is harmonic mean between $P$ and $Q$, then the value of $\frac{H}{P}+\frac{H}{Q}$ is :

• A. 2
• B. $\frac{P Q}{(P+Q)}$
• C. $\frac{(P+Q)}{P O}$
• D. None of these

Answer 1

Answer: (A)

If $h$ is harmonic mean between a and $b$, then $h=\frac{2 a b}{a+b}$.
Given $H$ is harmonic mean between $P$ and $Q$.
$\therefore \, H=\frac{2 P Q}{P+Q}$
$\Rightarrow \, \frac{H}{P}=\frac{2 Q}{P+Q}$
Also $ \frac{H}{Q}=\frac{2 P}{P+Q}$
$\therefore \, \frac{H}{P}+\frac{H}{Q}=\frac{2(P+Q)}{P+Q}=2$