Numerical answer
A vessel contains 80 litres of pure milk. 8 litres are drawn off and replaced with water. This operation is carried out three times in all. How many litres of milk remain in the vessel at the end?
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Answer: 58.32
Each operation removes 8/80 = 1/10 of whatever mixture is present, so the milk is multiplied by (1 − 1/10) = 9/10 each time; the volume stays at 80 litres.
Milk after 3 operations = 80 × (9/10)³ = 80 × 0.729 = 58.32 litres.
Formula: Final quantity = Initial × (1 − x/V)ⁿ, where x litres are replaced from a vessel of V litres, n times.
Milk after 3 operations = 80 × (9/10)³ = 80 × 0.729 = 58.32 litres.
Formula: Final quantity = Initial × (1 − x/V)ⁿ, where x litres are replaced from a vessel of V litres, n times.
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