Question
A container has a mixture of two liquids, A and B, in
the ratio of 5:3. If 16 liters of the mixture are removed and replaced with 16 liters of liquid B, the ratio of liquids A and B becomes 3:5. Find the initial quantity of liquid A in the container.Solution
ATQ, Let the initial quantity of liquid A be 5x liters and liquid B be 3x liters. After removing 16 liters, 10 liters of A and 6 liters of B are removed. The remaining amounts are: Liquid A: 5x - 10 liters. Liquid B: 3x - 6 liters. After adding 16 liters of liquid B, the new amount of liquid B is 3x + 10 liters. Given the new ratio of A to B is 3:5: (5x - 10) / (3x + 10) = 3 / 5. Cross-multiplying and solving: 25x - 50 = 9x + 30, 16x = 80, so x = 5. Thus, the initial quantity of liquid A is 5 × 5 = 25 liters.
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