A bucket contains 1 litre of milk

Question

A bucket contains 1 litre of milk. A milkman removes 10% of the content of the bucket and
replaces it with water. The next day the milkman again does the same operation and removes
10% of the contents of the bucket and replaces it with water. He then sells the one litre of milk
to a customer at the rate of $12 per litre. If the milkman had purchased the milk at $10 per litre
what is his profit percentage on his cost price keeping in mind that due to his mixing he was
able to save some additional milk?
(A)20%
(B) 48.15%
(C)50%
(D)55.45%
(E)60%

mikemcgarry · Answer

Dear sdpp143, I'm happy to respond.

First of all, here's a blog on mixture problems on the GMAT: https://magoosh.com/gmat/2012/gmat-solu ... -problems/ Something strikes me as peculiar about this problem. On the first day, the milkman withdraws pure milk, and replaces it with water. That 10% of pure milk he withdraws he can resell or use as pure milk somewhere else. On the second say, the milkman withdraws 0.1 liter, and what he withdraws is a 90% milk mixture. It's unclear what he can do with this mixture --- he can't use it as pure milk, and there's no reasonable way to extract the pure milk from this mixture. Therefore, it's unclear if this is milk that the milkman has "saved", in any meaningful way. That's strikes me as a very important problem --- are we figuring out his profit purely on the basis of the mixture he sales, or on the ratio of usable pure milk he has after the transaction as well??? In this sense, this strikes me as a poorly written problem. If we ignore this problem, after the second day, what's left in the bucket is a 81% milk mixture. He spend 81% of $10 on the milk in that, or $8.10, and he sells it for $12. Well, from $8.00 to $12.00 is a 50% increase, so from $8.10 to $12.00 must be slightly less than 50%. Without an exact calculation, it's easy to arrive at the answer they want, (B) . Again, that answer assumes that milkman loses absolutely nothing in the second amount he withdrew, the 0.1 liter of 90% milk mixture, even though he can no longer treat this as pure milk and even though it would be impossible to extract the pure milk from it. It strikes me that the question writer did not properly think through these issues. I don't know what the source it, but on the basis of this question, I am not impressed. Let me know if you have any further questions. Mike

A bucket contains 1 litre of milk

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