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CAT 2017 Slot 1 · Quant · Mixtures and Alligation · medium

How much milk (in litres) is left in the vessel at the end?

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?
  1. A. 42.00
  2. B. 43.74
  3. C. 44.16
  4. D. 45.00
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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.
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Original question written in the CAT 2017 Slot 1 pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake