# How to solve this problem on alligations with a precision?

Problem: " A milkman brings 100 litres pure milk from a daily farmer and he sells 10 litres of it to the first customer, then he refills his vessel by adding 10 litres water. After this, he proceeds to the next house and sells 10 litres of it to the second customer and then he refills his vessel again by adding 10 litres of water. Thus, every time he sells 10 litres of milk-pure or impure-he keeps on replacing it with 10 litres of pure water. Maximum how many customers can get at least 50% milk in the mixture that they purchase from this milkman?"

I am trying the problem and getting the value of 6 but the answer is 7. Where did I get it wrong?

• This milkman should be in jail. Dec 26, 2021 at 6:47
• @markvs Thug life :P Dec 26, 2021 at 6:56

After each sale, the milk concentration is $$.9$$ times what it was previously. We have $$.9^6=.53>.5$$ and $$.9^7=.49...<.5$$ so this milkman (who should definitely be in jail) can make sales with milk at concentration $$1,.9,(.9)^2,...,(.9)^6$$. That's $$7$$ customers.