Numerical answer
A vessel contains 60 litres of pure milk. 12 litres are taken out and replaced with water. This operation is performed three times in all. How many litres of milk are left in the vessel? (Enter the answer correct to two decimal places.)
Show answer and solution
Answer: 30.72
Each operation keeps (60 − 12)/60 = 4/5 of the milk present.
After n operations, milk = initial × (1 − removed/total)ⁿ.
Milk after 3 operations = 60 × (4/5)³ = 60 × 64/125 = 30.72 litres.
Why it works: every time, the removed 12 L has the same composition as the mixture, so the same fraction (1/5) of the milk leaves each time.
Tip: use this formula for any repeated remove-and-replace problem.
After n operations, milk = initial × (1 − removed/total)ⁿ.
Milk after 3 operations = 60 × (4/5)³ = 60 × 64/125 = 30.72 litres.
Why it works: every time, the removed 12 L has the same composition as the mixture, so the same fraction (1/5) of the milk leaves each time.
Tip: use this formula for any repeated remove-and-replace problem.
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