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In a vessel, a mixture of milk and coffee is in the ratio 9 ∶ 1. If 20 liters of the mixture is taken out and same quantity of coffee is poured into the vessel, the ratio of milk and coffee becomes 5 ∶ 2. Find the original quantity of Milk in the vessel?1). 79.3 liters2). 82.3 liters3). 87.3 liters4). 77.3 liters |
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Answer» LET the ORIGINAL quantity of milk be 9X and coffee be x According to the question, $(\frac{{\left( {9x - 20} \right) \times \frac{9}{{10}}\;}}{{\left( {x - 20} \right) \times \frac{1}{{10}} + 20}} = \frac{5}{2})$ $(\RIGHTARROW \frac{{9x - 18\;}}{{x + 18}} = \frac{5}{2})$ ⇒ (9x – 18) × 2 = (x + 18) × 5 ⇒ 18x – 36 = 5x + 90 ⇒ 13x = 126 ⇒ x = 9.69 or 9.7 ∴ Original quantity of milk = 9x = 9 × 9.7 = 87.3 liters |
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