A chemist has 90 liters of a solution with alcohol and water in the ratio 1:2. How much water must be removed and replaced with alcohol to make the ratio 2:3?
6 liters
In 90 liters of solution with alcohol : water = 1 : 2, alcohol = 30 liters and water = 60 liters.
Let x liters of water be removed and replaced with x liters of alcohol. Then alcohol = (30 + x) liters and water = (60 − x) liters.
(30 + x) : (60 − x) = 2 : 3 ⇒ 3(30 + x) = 2(60 − x) ⇒ 90 + 3x = 120 − 2x ⇒ 5x = 30 ⇒ x = 6.
Hence, the answer is 6 liters.
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