litres are removed from litres of solution of milk and water having ratio of milk and water as and replaced with water. This operation is done a total of three times. What is the quantity of milk in the solution?
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This one took me way longer than it should have. I kept trying to track milk and water separately through all three replacements and it got messy fast.
Same here. Did you eventually just track the milk fraction staying multiplied by the same factor each time?
Yeah that's the clean way. The water part is just noise since we only care about how the milk gets diluted down.
Wait, why is the answer in eighths? I got a decimal and assumed I messed up somewhere.
245/8 is 30.625, so the choices are just formatted as fractions. Don't let that throw you off.
Oh that makes sense, I thought I was missing some step that forces the denominator.
Solid 700-ish question IMO. The trick is realizing you remove 10 from 80, so each time 7/8 of the milk remains. Three times means (7/8)^3 of the original milk.
Right, and original milk is 4/7 of 80. Multiply those and you're basically done.
Nice, I was overcomplicating it by recomputing the ratio each round.
Is the removed mixture always in the same milk-to-water ratio as the current solution? That's the part I always second-guess.
Yes, that's the whole assumption with these replacement problems, assuming it's well mixed.
What it tests
Your ability to reason about weighted averages and the composition of mixtures.
Common trap
Averaging the percentages of two solutions without weighting by their volumes.