a certain quantity of 45 % solution is replaced with 25 % solution such that the new concentration is 35 % . what is the fraction of the solution that was replaced ?
"let ' s say that the total original mixture a is 100 ml the original mixture a thus has 45 ml of alcohol out of 100 ml of solution you want to replace some of that original mixture a with another mixture b that contains 25 ml of alcohol per 100 ml . thus , the difference between 45 ml and 25 ml is 20 ml per 100 ml of mixture . this means that every time you replace 100 ml of the original mixture a by 100 ml of mixture b , the original alcohol concentration will decrease by 20 % . the question says that the new mixture , let ' s call it c , must be 35 % alcohol , a decrease of only 10 % . therefore , 10 out of 20 is 1 / 2 and c is the answer ."
inverse(add(divide(subtract(35, 25), subtract(45, 35)), const_1))