Numerical answer
A container is full with 80 litres of pure milk. 8 litres are drawn out and replaced with water. This operation is performed a total of three times. How many litres of milk are left in the container at the end?
Show answer and solution
Answer: 58.32
Each operation removes 8/80 = 1/10 of whatever is in the container, so the milk left is multiplied by 9/10 each time.
Milk after three operations = 80 × (9/10)³ = 80 × 0.729 = 58.32 litres.
Why not 80 − 24 = 56? After the first replacement the 8 litres drawn out are not pure milk, so less than 8 litres of milk is removed each subsequent time.
Formula: Final = Initial × (1 − x/V)ⁿ.
Milk after three operations = 80 × (9/10)³ = 80 × 0.729 = 58.32 litres.
Why not 80 − 24 = 56? After the first replacement the 8 litres drawn out are not pure milk, so less than 8 litres of milk is removed each subsequent time.
Formula: Final = Initial × (1 − x/V)ⁿ.
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