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
Question:
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
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
Options
Answer: 30
Explanation:
Let initial water = x litres, milk = 300 − x litres. Solution removed = 2x litres → milk left = (300 − x)(1 − x/150) Refill with water → total water = x(3 − x/150) Milk fraction after refill = 72% → (300 − x)(1 − x/150)/300 = 0.72 Solve: (300 − x)(150 − x)/150 = 216 → (300 − x)(150 − x) = 32400 x² − 450x + 12600 = 0 → x = [450 ± √152100]/2 → x = 30 Answer: 30 liters
Explanation:
Let initial water = x litres, milk = 300 − x litres. Solution removed = 2x litres → milk left = (300 − x)(1 − x/150) Refill with water → total water = x(3 − x/150) Milk fraction after refill = 72% → (300 − x)(1 − x/150)/300 = 0.72 Solve: (300 − x)(150 − x)/150 = 216 → (300 − x)(150 − x) = 32400 x² − 450x + 12600 = 0 → x = [450 ± √152100]/2 → x = 30 Answer: 30 liters
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