CAT 2024 Slot 3 QA Q8 Percentages & Profit-Loss

Question 8 of the Quantitative Ability (QA) section, CAT 2024 Slot 3, with CAT's official answer and a worked solution.

After two successive increments, Gopal's salary became 187.5% of his initial salary. If the percentage of salary increase in the second increment was twice of that in the first increment, then the percentage of salary increase in the first increment was
  1. A
    27.5
  2. B
    30
  3. C
    25
  4. D
    20

Answer: (C) 25 Percentages & Profit-Loss MCQ

Solution

  1. Let the first increment be \(x\): \((1+x)(1+2x) = 1.875\).
  2. \(2x^2 + 3x - 0.875 = 0 \Rightarrow 16x^2 + 24x - 7 = 0 \Rightarrow x = \frac{-24 + 32}{32} = 0.25\). So 25%.

Shortcut. Try options: \(1.25 \times 1.5 = 1.875\).

Same concept in other years

See every question on Two successive percentage changes with related rates.

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