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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?

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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 liters
2). 82.3 liters
3). 87.3 liters
4). 77.3 liters


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Answered by on | Votes 0 |

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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