Question

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

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

Answer 1

Answer: (A)

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