Let a machine overcome a load $\mathrm{L}$ by the application of an effort $\mathrm{E}$ . In time $\mathit{t}$ , let the displacement of effort be ${\mathit{d}}_{\mathrm{E}}$ and the displacement of load be ${\mathit{d}}_{\mathrm{L}}$ .

$=\mathrm{E}\times {\mathit{d}}_{\mathrm{E}}$
Work output $=$ Load $\times$ displacement of load
$=\mathrm{L}\times {\mathit{d}}_{\mathrm{L}}$
Efficiency
$=\frac{\mathrm{L}\times {\mathit{d}}_{\mathrm{L}}}{\mathrm{E}\times {\mathit{d}}_{\mathrm{E}}}=\frac{\mathrm{L}}{\mathrm{E}}\times \frac{{\mathit{d}}_{\mathrm{L}}}{{\mathit{d}}_{\mathrm{E}}}$
$=\frac{\mathrm{L}}{\mathrm{E}}\times \frac{1}{{\mathit{d}}_{\mathrm{E}}∕{\mathit{d}}_{\mathrm{L}}}$
But M.A. and $\frac{{\mathit{d}}_{\mathrm{E}}}{{\mathit{d}}_{\mathrm{L}}}=$ V.R.


Thus, the mechanical advantage of a machine is equal to the product of its efficiency and Velocity Ratio.