Five hundred liters of a solution was available but the solu

Five hundred liters of a solution was available, but the solution was 80% alcohol. Neil needed a solution which was 75% alcohol. How many liters of alcohol had to be extracted so that the solution would be 75% alcohol? A solution of 49% alcohol is to be mixed with a solution of 21% alcohol

Solution

Let x liters of alcohol be extracted from 500 liters of 80 % solution , so as to have a 75 % solution. The quantity of alcohol in 500 liters of 80 % solution is 500*0.80 = 400 liters. After extracting x liters of alcohol from 500 liters of 80 % solution, 500-x liters of 75 % solution remains so that (500-x)*0.75 = 400-x or, 375 -0.75x = 400-x or, x -0.75x = 400-375 or, 0.25x = 25. Hence x = 25/0.25 = 100. Thus, 100 liters of alcohol has to be extracted from 500 liters of 80 % solution , so as to have a 75 % solution.

Note:

After extracting 100 liters of alciohol from a 500 liter solution, which contains 400 liters of alcohol, what remains is a 400 liter solution containing 300 liters of alcohol. The concentration of alcohol in the remaining solution is (300/400 )*100 = 75 %. Thus, our answer stands verified.