CAT 2023 Slot 1 QA Q13 Percentages & Profit-Loss

Question 13 of the Quantitative Ability (QA) section, CAT 2023 Slot 1, with CAT's official answer and a worked solution.

Gita sells two objects A and B at the same price such that she makes a profit of 20% on object A and a loss of 10% on object B. If she increases the selling price such that objects A and B are still sold at an equal price and a profit of 10% is made on object B, then the profit made on object A will be nearest to
  1. A
    42%
  2. B
    47%
  3. C
    45%
  4. D
    49%

Answer: (B) 47% Percentages & Profit-Loss MCQ

Solution

  1. Let the common SP be \(S\). Cost of A \(= \frac{S}{1.2}\), cost of B \(= \frac{S}{0.9}\).
  2. New common SP \(= 1.1\times\frac{S}{0.9}\) (10% profit on B).
  3. Ratio for A: \(\frac{1.1S/0.9}{S/1.2} = \frac{1.32}{0.9} = 1.4667\).
  4. Profit on A \(\approx 46.7\% \approx 47\%\).

Shortcut. Take \(S=36\): costs 30 and 40, new SP 44, profit on A \(= \frac{14}{30} = 46.7\%\).

Same concept in other years

See every question on Two items at different profit/loss rates: overall profit equation.

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