Question

If $H$ be 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. $\frac{P+Q}{PQ}$
• D. none of these

Answer 1

The correct option is A $2$

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

$\therefore \frac{H}{P}+\frac{H}{Q}=(\frac{1}{P}+\frac{1}{Q})H$

$=\left(\frac{P+Q}{PQ}\right)\left(\frac{2PQ}{P+Q}\right)$

$=2$