In 80 litres pure milk, 8 litres of milk is replaced by water if this process is repeated two times then what will be the ratio of milk and water in the final mixture?
In 80 litres pure milk, 8 litres of milk is replaced by water if this process is repeated two times then what will be the ratio of milk and water in the final mixture?
Correct Answer: [81:19]
Explanation:
We start with 80 litres of pure milk. Each time we replace 8 litres of milk with water, the concentration of milk decreases. This process is repeated twice.
Steps:
First Replacement:
Milk removed: 8 litres
Water added: 8 litres
Remaining milk: \(80- 8 = 72\) litres
Water present: 8 litres
Second Replacement:
The mixture now has 72 litres milk and 8 litres water. The ratio of milk to water is \(72:8 = 9:1\)
When 8 litres of the mixture is removed:
Milk removed: \(\frac{9}{10} \times 8 = 7.2\) litres
Water removed: \(\frac{1}{10} \times 8 = 0.8\) litres
Remaining milk: \(72- 7.2 = 64.8\)litres
Remaining water: \(8- 0.8 + 8 = 15.2\) litres
Final mixture:
Milk: 64.8 litres
Water: 15.2 litres
Ratio of milk to water: \(64.8:15.2 = 81:19\)
Final Answer: \(\boxed{81:19}\)
