A dishonest hair dresser uses a mixture having 6 parts of pure aftershave lotion and 4 parts of pure water. After taking out some quantity of the mixture, he adds equal amount of pure water to the remaining mixture such that the amount of aftershave lotion and water becomes equal. What part of the mixture was taken out?

Let quantity of pure aftershave lotion= 6kg and quantity of pure water=4kg Therefore, total quantity of the mixture=10kg Again let x kg of mixture is taken out of 10 kg of mixture. Now, the amount of aftershave lotion left=(6-(6x/10)) kg And the amount of water left=(4-(4x/10)) kg Thus, the amount of water after adding x kg of water becomes (4-(4x/10)+x)kg=(4+(6x/10)) kg According to the question, (6-(6x/10))=(4+(6x/10)) 12x/10=2 x=10/6 Therefore, 1/6 of the10 kg mixture is taken out. It is the correct answer.