Question
A jar has 360 liters of a syrup and water mixture in the
ratio 3:2 (syrup : water). If x liters of this mixture is drawn out and replaced with water, then the ratio of water to syrup becomes 4:5. Find x?Solution
ATQ, Syrup in the initial mixture = 360 * 3/(3 + 2) = 360 * 3/5 = 216 liters Water in the initial mixture = 360 – 216 = 144 liters (216 – x * 3/(3 + 2)) / (144 – x * 2/(3 + 2) + x) = 5/4 [since final syrup : water = 5 : 4 ⇒ syrup / water = 5/4] (216 – 3x/5) / (144 – 2x/5 + x) = 5/4 (216 – 3x/5) / (144 + 3x/5) = 5/4 4(216 – 3x/5) = 5(144 + 3x/5) 864 – 12x/5 = 720 + 15x/5 864 – 720 = 15x/5 + 12x/5 144 = 27x/5 x = 144 * 5 / 27 x = 720 / 27 x = 80/3 x = 80/3 liters
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