Numerical answer
A vessel contains 80 litres of pure milk. 16 litres are drawn out and replaced by water. This operation is carried out three times in all. How many litres of milk remain in the vessel at the end?
Show answer and solution
Answer: 40.96
Each operation removes 16/80 = 1/5 of the current mixture, so milk is multiplied by 4/5 every time.
Milk left = 80 × (4/5)³ = 80 × 64/125 = 40.96 litres.
(Water = 80 − 40.96 = 39.04 litres.)
Formula: after n replacements of x litres from a V-litre vessel, pure liquid left = V(1 − x/V)ⁿ.
Milk left = 80 × (4/5)³ = 80 × 64/125 = 40.96 litres.
(Water = 80 − 40.96 = 39.04 litres.)
Formula: after n replacements of x litres from a V-litre vessel, pure liquid left = V(1 − x/V)ⁿ.
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