75% of 40 liters is 30 liters of pure acid, which you got. Then you ask the question: 30 liters of acid is 60% of what? 30 = .60x= x 50 = x So if you add enough water to make it 50 liters, those 30 liters of pure acid would make it 60% of the 50. Therefore to make the 40 liters 50 liters you need to add 10 liters of water. ----------------------------------------------------------- However that method will only work when you are adding water. Below is a method that will work when you add any percentage solution to any other percentage solution. In your case water is considered a 0% solution but the method will work in all cases, not just for adding water. Just put the percentage of acid in what you're adding, which may be anywhere from 0% to 100%, where the 0% is below. If you were adding pure acid, then you would put 100% where the 0% is below LITERS OF PERCENT LITERS OF LIQUID OF ACID PURE ACID --------------------------------------------------- Starting solution 40 75% 75%(40) Added solution x 0% 0%(x) Final solution 40+x 60% 60%(40+x) 75%(40) + 0%(x) = 60%(40+x) .75(40) + .00(x) = .60(40+x) 30 + 0 = 24 + .60x 30 = 24 + .60x 6 = .60x 10 = x answer: 10 liters of water. Edwin