sukhman wrote:A vessel has 500 ml of alcohol . 50 ml of alcohol is removed and 50 ml of water is poured into the vessel ( bringing the volume of the mixture in the vessel back to 500 ml ). If this operation is recreated another 2 times , what is the percentage of alcohol in the vessel at the end ?
If we're removing 50 ml of the resulting solution each time, then here's one approach:
Let's keep track of the alcohol with each move.
Start:
500 ml of alcohol
Remove 50ml from vessel:
Left with 450 ml of alcohol
Add 50ml of water:
Still have 450 ml of alcohol
NOTE: the mixture is now
90% alcohol [since 450/500 = 90%]
Remove 50ml from vessel: 90% of this is alcohol. So, of the 50ml of mixture, 45 mls are alcohol. So, we are removing 45 mls of alcohol
We're left with 405 ml of alcohol
Add 50ml of water:
Still have 405 ml of alcohol
NOTE: the mixture is now
81% alcohol [since 405/500 = 81%]
Remove 50ml from vessel: 81% of this is alcohol. So, of the 50ml of mixture, 40.5 mls are alcohol. So, we are removing 40.5 mls of alcohol
We're left with 364.5 ml of alcohol
Add 50ml of water:
Still have 364.5 ml of alcohol
364.5/500 = 729/1000 = 72.9/100 = [spoiler]72.9%[/spoiler]
Cheers,
Brent
