Single correct option
A vessel contains 60 litres of pure milk. 6 litres are drawn out and replaced with water. This operation is performed three times in all. How much milk (in litres) is left in the vessel at the end?
- A. 42.00
- B. 43.74
- C. 44.16
- D. 45.00
Show answer and solution
Answer: (B) 43.74
Each operation removes 6/60 = 1/10 of whatever mixture is present, so the milk is multiplied by (1 − 1/10) = 9/10 each time; the total volume stays 60 L.
Milk left = 60 × (9/10)³ = 60 × 0.729 = 43.74 litres.
Formula: Final quantity = Initial × (1 − x/V)ⁿ, where x is drawn each time from volume V, repeated n times.
Simply subtracting 3 × 6 = 18 litres (giving 42) is wrong because the second and third draws remove diluted mixture, not pure milk.
Milk left = 60 × (9/10)³ = 60 × 0.729 = 43.74 litres.
Formula: Final quantity = Initial × (1 − x/V)ⁿ, where x is drawn each time from volume V, repeated n times.
Simply subtracting 3 × 6 = 18 litres (giving 42) is wrong because the second and third draws remove diluted mixture, not pure milk.
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