CAT 2025 Slot 2 QA Q13 Ratio, Mixtures & Averages

Question 13 of the Quantitative Ability (QA) section, CAT 2025 Slot 2, with CAT's official answer and a worked solution.

The ratio of expenditures of Lakshmi and Meenakshi is 2 : 3, and the ratio of income of Lakshmi to expenditure of Meenakshi is 6 : 7. If excess of income over expenditure is saved by Lakshmi and Meenakshi, and the ratio of their savings is 4 : 9, then the ratio of their incomes is
  1. A
    5 : 6
  2. B
    3 : 5
  3. C
    7 : 8
  4. D
    2 : 1

Answer: (B) 3 : 5 Ratio, Mixtures & Averages MCQ

Solution

  1. Let expenditures be \(2k\) (L) and \(3k\) (M). L's income \(= \frac67 \times 3k = \frac{18k}{7}\).
  2. L's savings \(= \frac{18k}{7} - 2k = \frac{4k}{7}\), so M's savings \(= \frac94 \cdot \frac{4k}{7} = \frac{9k}{7}\).
  3. M's income \(= 3k + \frac{9k}{7} = \frac{30k}{7}\).
  4. Ratio of incomes \(= 18 : 30 = 3 : 5\).

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