Question

If $H$ is the 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. $\frac{1}{2}$
• D. $\frac{P+Q}{PQ}$

Answer 1

The correct option is A $2$

Since, $H$ is the harmonic mean between $P$ and $Q$

$\therefore H=\frac{2PQ}{P+Q}$

$\Rightarrow \frac{H}{P}=\frac{2Q}{P+Q}$

Also, $\frac{H}{Q}=\frac{2P}{P+Q}$

$\therefore \frac{H}{P}+\frac{H}{Q}$

$=\frac{2Q}{P+Q}+\frac{2P}{P+Q}$

$=\frac{2P+2Q}{P+Q}=2$

Hence, option A is correct.