CAT 2025 Slot 2 QA Q17 Ratio, Mixtures & Averages

Question 17 of the Quantitative Ability (QA) section, CAT 2025 Slot 2, with CAT's official answer and a worked solution.

A mixture of coffee and cocoa, 16% of which is coffee, costs Rs 240 per kg. Another mixture of coffee and cocoa, of which 36% is coffee, costs Rs 320 per kg. If a new mixture of coffee and cocoa costs Rs 376 per kg, then the quantity, in kg, of coffee in 10 kg of this new mixture is
  1. A
    4
  2. B
    6
  3. C
    2.5
  4. D
    5

Answer: (D) 5 Ratio, Mixtures & Averages MCQ

Solution

  1. Let coffee cost \(c\) and cocoa \(k\) per kg: \(0.16c + 0.84k = 240\), \(0.36c + 0.64k = 320\).
  2. Subtract: \(0.2(c - k) = 80 \Rightarrow c - k = 400\). Then \(k + 0.16 \times 400 = 240 \Rightarrow k = 176\), \(c = 576\).
  3. New mixture with coffee fraction \(f\): \(176 + 400f = 376 \Rightarrow f = 0.5\).
  4. Coffee in 10 kg \(= 5\) kg.

Shortcut. Price is linear in coffee %: +20 points costs Rs 80, so Rs 4 per point; 376 is 34 points above 240's 16%, i.e. 50%.

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