Numerical answer
A container holds 80 litres of pure milk. 16 litres are drawn out and replaced with water. This operation is performed two more times (three operations in all). How many litres of milk remain in the container at the end?
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Answer: 40.96
Each operation removes 16/80 = 1/5 of whatever mixture is present, so the milk is multiplied by (1 − 1/5) = 4/5 each time, while the total volume stays 80 litres.
Milk after 3 operations = 80 × (4/5)³ = 80 × 64/125 = 40.96 litres.
Tip: Repeated replacement formula: Final = Initial × (1 − x/V)ⁿ, where x is the quantity drawn each time from volume V.
Milk after 3 operations = 80 × (4/5)³ = 80 × 64/125 = 40.96 litres.
Tip: Repeated replacement formula: Final = Initial × (1 − x/V)ⁿ, where x is the quantity drawn each time from volume V.
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