CAT 2024 Slot 1 QA Q6 Ratio, Mixtures & Averages

Question 6 of the Quantitative Ability (QA) section, CAT 2024 Slot 1, with CAT's official answer and a worked solution.

In September, the incomes of Kamal, Amal and Vimal are in the ratio 8 : 6 : 5. They rent a house together, and Kamal pays 15%, Amal pays 12% and Vimal pays 18% of their respective incomes to cover the total house rent in that month. In October, the house rent remains unchanged while their incomes increase by 10%, 12% and 15%, respectively. In October, the percentage of their total income that will be paid as house rent, is nearest to
  1. A
    14.84
  2. B
    12.75
  3. C
    13.26
  4. D
    15.18

Answer: (C) 13.26 Ratio, Mixtures & Averages MCQ

Solution

  1. Take September incomes as 800, 600, 500 (total 1900).
  2. Rent \(= 15\%\cdot800 + 12\%\cdot600 + 18\%\cdot500 = 120 + 72 + 90 = 282\).
  3. October incomes: \(880,\ 672,\ 575\); total \(= 2127\).
  4. Rent share \(= \frac{282}{2127} \times 100 \approx 13.26\%\).

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