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

Answer: (A)

Given : H is the harmonic mean between P & Q
$\therefore H=\frac{2PQ}{P+Q}\Rightarrow \frac{1}{H}=\frac{P+Q}{2PQ}$
$\Rightarrow \frac{2}{H}=\frac{1}{Q}+\frac{1}{P}\Rightarrow \frac{H}{P}+\frac{H}{Q}=2$