How long does it take to lose 20lb binging and purging?

Don't. You may never lose wt doing this as you are still binging. Not only are you unlikely to loose wt you are risking electrolyte imbalances that can result in cardiac arrhythmias and death, your teeth rot from the stomach acid, your checks get like a chimpmunk from swollen salivary glands, stomach acid burns your esophogus causing ulcers and pain. There are better ways, get help.