Question
A container contains a mixture of two liquids, A and B,
in the ratio of 5:7. If 15 liters of liquid A is replaced by liquid B, the ratio becomes 1: 2. How many liters of liquid A was there initially in the container?Solution
Let the initial volume of liquid A and B be 5x and 7x, respectively. After 15 liters of liquid A is replaced by liquid B, the volume of liquid A becomes (5x - 15) and the volume of liquid B becomes (7x + 15). We are told the new ratio of A to B is 1: 2, so: (5x - 15) / (7x + 15) = 1/2. Cross-multiply: 2(5x - 15) = (7x + 15), 10x - 30 = 7x + 15, 10x - 7x = 30 + 15, 3x = 45, x = 15 Thus, the initial volume of liquid A = 5x = 5 × 15 = 75 liters.
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25, 38, 53, 74, 97, 126
Find the wrong number in the given number series.
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2592 1300 656 331 169.5 88.75
...79, 152, 231, 314, 405, 500
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237, 526, 165, 608, 77, 702
75, 450, 225, 1330, 675, 4050
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2847, 2954, 2799, 3088, 2727, 3256
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13, 20, 31, 44, 62, 80
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1759, 1765, 1785, 2047, 2099, 2209
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