Question

If $2x=3y=12z$ then $\frac{1}{z}=\frac{1}{y}+\frac{m}{x}$.Find $2m$

Answer 1

Given:-

$2x=12z$

$\Rightarrow x=6z$

$3y=12z$

$\Rightarrow y=4z$

$\therefore \frac{1}{z}=\frac{1}{y}+\frac{m}{x}$

$\Rightarrow \frac{1}{z}=\frac{1}{4z}+\frac{m}{6z}$

$\Rightarrow 1=\frac{1}{4}+\frac{m}{6}$

$\Rightarrow 1=\frac{3+2m}{12}$

$\Rightarrow 3+2m=12$

$\Rightarrow 2m=12-3$

$\Rightarrow m=\frac{9}{2}$

$\therefore 2m=9$