Question
The ratio of juice to soda in an 84-liter mixture (juice
+ soda) is 9:5. A certain quantity of this mixture is taken out and replaced with the same quantity of soda. If the final mixture has a ratio of 3:4 for juice and soda, respectively, determine the quantity of the mixture that has been taken out.Solution
ATQ, Initial quantity of Juice in the mixture = 84 × (9/14) = 54 liters Initial quantity of Soda in the mixture = 84 × (5/14) = 30 liters Let the quantity of mixture that has been taken out be ‘14m’ liters So, quantity of Juice that has been taken out = 14m × (9/14) = ‘9m’ liters Quantity of Soda that has been taken out = 14m × (5/14) = ‘5m’ liters According to question: {(54 – 9m)/(30 – 5m + 14m)} = (3/4) Or, 4 × (54 – 9m) = 3 × (30 + 9m) Or, 72 – 12m = 30 + 9m Or, 21m = 42 Or, m = 2 Quantity of mixture that has been taken out = 14 × 2 = 28 liters.
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