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
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