CAT 2023 Quant was dominated by Algebra followed by Arithmetic. In Arithmetic, the questions were dominated by topics like **Speed-time-distance**, **Mixture and Alligations**. This year, there was a surprise. The questions from **Geometry** were relatively on the lower side as compared to the previous years. There were 8 TITA Qs this year. Overall this section was at a medium level of difficulty.

Question 13 : 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

- 42%
- 47%
- 45%
- 49%

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Let A be the cost price of object A and B be the cost price of object B.

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.

Therefore, 1.2 × A = 0.9 × B

4 A = 3 B

B = \( \frac { 4 } { 3 } \) A

To sell object B at a profit of 10%, the selling price of B must be 1.1 B or \( \frac { 11 } { 10 } \) B

Object A is sold at the same price as object B, that is, \( \frac { 11 } { 10 } \) B = \( \frac { 11 } { 10 } \times \frac { 4 } { 3 } \) A = 1.466 A

The profit obtained on object A in such a trade will be 46.66% or nearly 47%.

Choice B is the correct answer.

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