Numerical answer
A vessel contains 80 litres of pure milk. 8 litres are drawn out and replaced with water. This operation is done three times in all. How many litres of milk remain in the vessel?
Show answer and solution
Answer: 58.32
Each operation removes 8/80 = 1/10 of the contents, so the milk left is multiplied by 9/10 every time.
Milk after 3 operations = 80 × (9/10)³ = 80 × 0.729 = 58.32 litres.
Why this works: water added later does not change how much milk there is. Each draw removes the same fraction of whatever milk is present.
Formula: Final quantity = Initial × (1 − x/V)ⁿ, where x litres are replaced n times in a vessel of V litres.
Milk after 3 operations = 80 × (9/10)³ = 80 × 0.729 = 58.32 litres.
Why this works: water added later does not change how much milk there is. Each draw removes the same fraction of whatever milk is present.
Formula: Final quantity = Initial × (1 − x/V)ⁿ, where x litres are replaced n times in a vessel of V litres.
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