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. $\frac{P+Q}{PQ}$
• D. None of these

Answer 1

Answer: (A)

$2$

If $h$ is the harmonic mean of $a$ and $b$, then
$h=\frac{2ab}{a+b}$
Given, $H$ is the harmonic mean between $P$ and $Q$.
$\therefore H=\frac{2PQ}{P+Q}$
$\Rightarrow \frac{H}{P}=\frac{2Q}{P+Q}....\left(i\right)$
Also, $\frac{H}{Q}=\frac{2P}{P+Q}...\left(ii\right)$
Adding Eqs. (i) and (ii)
$\frac{H}{P}+\frac{H}{Q}=\frac{2(P+Q)}{(P+Q)}=2$.