Can someone help with this mixture question?I’m not sure how to solve it?
A certain amount of water was poured into a 300 litre container and the remaining portion of the container was filled with milk. Then an amount of this solution was taken out from the container which was twice the volume of water that was earlier poured into it, and water was poured to refill the container again. If the resulting solution contains 72% milk, then the amount of water, in litres, that was initially poured into the container was
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Asked by Karthik Iyer 5 months ago
Student at Kellogg
Faced the same type of question during GMAT prep. Here's how to solve it step by step.
- Let the water poured = x litres
- So milk = 300 – x litres
- Total taken out = 2x litres, so milk and water are removed in the same ratio
- Final milk = (300 – x) × (1 – 2x/300)
- Final milk is also given as 72 percent of 300, so 216 litres
- Now equate: (300 – x) × (1 – 2x/300) = 216
- Multiply and simplify the equation, you get a quadratic
- Solve to get x = 30 or 420, but 420 isn’t possible since the tank is only 300 litres
So the final answer is 30 litres of water was added at the start. Just need to be careful with the replacement logic and ratios.
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