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Vessel A contains \((2x + 360)\) litres of a milk-water mixture in the ratio \(7:5\), and vessel B contains 200 litres of a milk-water mixture in the ratio \(3:2\). If vessels A and B are mixed together, the resulting ratio of milk to water becomes \(47:33\). Find the value of \(x\).

1. 80
2. 100
3. 120
4. 125

Correct answer: 120

Solution

In vessel A, milk = \((2x+360)\times \frac{7}{12}\) and water = \((2x+360)\times \frac{5}{12}\). In vessel B, milk = 120 and water = 80. Using the final ratio \(47:33\), equate total milk and water in the combined mixture and solve for \(x\).

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