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Profit and Loss with Equal Selling Prices

CAT 2023 Slot 1 · Quantitative Ability · Medium · Arithmetic

This is a medium Quantitative Ability question from the CAT 2023 Slot 1 paper. It tests Arithmetic. The full answer key and a step-by-step explanation are below — try it yourself first, then reveal the solution.

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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

Explanation

Initial selling price =S= S.

  • CPA=S1.2=56SCP_A = \frac{S}{1.2} = \frac{5}{6}S
  • CPB=S0.9=109SCP_B = \frac{S}{0.9} = \frac{10}{9}S

New selling price S′S' gives 10% profit on B: S′=1.1×CPB=1.1×109S=119SS' = 1.1 \times CP_B = 1.1 \times \frac{10}{9}S = \frac{11}{9}S

Profit on A at selling price S′S': Profit%=S′−CPACPA×100%=(119S56S−1)×100%\text{Profit\%} = \frac{S' - CP_A}{CP_A} \times 100\% = \left(\frac{\frac{11}{9}S}{\frac{5}{6}S} - 1\right) \times 100\% =(119×65−1)×100%=(2215−1)×100%=715×100%≈46.67%≈47%= \left(\frac{11}{9} \times \frac{6}{5} - 1\right) \times 100\% = \left(\frac{22}{15} - 1\right) \times 100\% = \frac{7}{15} \times 100\% \approx 46.67\% \approx 47\%

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