Numerical answer
A cistern is filled with 80 litres of pure milk to begin with. On four separate occasions, 8 litres of the mixture currently in the cistern are drawn off and immediately topped up with water. How many litres of milk remain once all four replacements are complete?
Show answer and solution
Answer: 52.488
Each draw-and-refill removes 8/80 = 1/10 of whatever milk is currently present, so 9/10 of the milk survives each round.
Milk remaining after 4 rounds = 80 × (9/10)⁴ = 80 × 0.6561 = 52.488 litres.
Formula: Final quantity of original liquid = Initial × (1 − r/V)ⁿ, where r litres are replaced each time from a vessel of volume V, n times.
A common error is subtracting 8 litres of milk four times (giving 48), which ignores that later draws remove water too.
Milk remaining after 4 rounds = 80 × (9/10)⁴ = 80 × 0.6561 = 52.488 litres.
Formula: Final quantity of original liquid = Initial × (1 − r/V)ⁿ, where r litres are replaced each time from a vessel of volume V, n times.
A common error is subtracting 8 litres of milk four times (giving 48), which ignores that later draws remove water too.
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