a certain quantity of 70 % 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 70 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 70 ml and 25 ml is 45 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 45 % . the question says that the new mixture , let ' s call it c , must be 35 % alcohol , a decrease of only 35 % . therefore , 35 out of 45 is 7 / 9 and e is the answer .
inverse(add(divide(subtract(35, 25), subtract(70, 35)), const_1))