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CAT 2025 Slot 2 · Quant · Mixtures and Alligation · medium

A shopkeeper mixes milk solution A (milk:water = 5:1) with milk solution B (milk:water = 2:1) to obtain a mixture in which milk:water = 3:1. In what…

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A shopkeeper mixes milk solution A (milk:water = 5:1) with milk solution B (milk:water = 2:1) to obtain a mixture in which milk:water = 3:1. In what ratio must A and B be mixed?
  1. A. 1:1
  2. B. 1:2
  3. C. 2:1
  4. D. 2:3
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Answer: (A) 1:1

Milk fraction in A = 5/6, in B = 2/3, required fraction in mixture = 3/4. By alligation, A:B = (target − B) : (A − target) = (3/4 − 2/3) : (5/6 − 3/4) = (1/12) : (1/12) = 1:1. Check: mixing A and B in equal parts gives milk fraction (5/6 + 2/3)/2 = (5/6+4/6)/2 = (9/6)/2 = 3/4, which matches.
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Original question written in the CAT 2025 Slot 2 pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake