Numerical answer
A vessel contains 80 litres of a mixture of milk and water in the ratio 3 : 1. Sixteen litres of the mixture are removed and replaced with water. This operation (remove 16 litres of the mixture, replace with 16 litres of water) is performed once more. What percentage of the final mixture is milk?
Show answer and solution
Answer: 48
Initially milk = 60 L (3/4 of 80). Each operation removes 16/80 = 1/5 of the mixture, so the milk present is multiplied by (1 − 1/5) = 4/5 each time, while the total volume stays 80 L.
Milk after two operations = 60 × (4/5)² = 60 × 16/25 = 38.4 L.
Milk % = 38.4/80 × 100 = 48%.
Tip: for repeated replacement, the quantity of the original liquid = initial × (1 − x/V)ⁿ.
Milk after two operations = 60 × (4/5)² = 60 × 16/25 = 38.4 L.
Milk % = 38.4/80 × 100 = 48%.
Tip: for repeated replacement, the quantity of the original liquid = initial × (1 − x/V)ⁿ.
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