CAT 2023 Question Paper | Quant Slot 1

CAT Questions

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 12 : The salaries of three friends Sita, Gita and Mita are initially in the ratio 5 : 6 : 7, respectively. In the first year, they get salary hikes of 20%, 25% and 20%, respectively. In the second year, Sita and Mita get salary hikes of 40% and 25%, respectively, and the salary of Gita becomes equal to the mean salary of the three friends. The salary hike of Gita in the second year is

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Video Explanation

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Explanatory Answer

Let the initial salaries of Sita, Gita and Mita be 5x, 6x and 7x respectively.
After getting 20%, 25% and 20% salary hikes respectively, their salaries become 6x, 7.5x and 8.4x respectively.
In the second year we don’t know Gita’s hike but Sita and Mita get 40% and 25% hikes respectively.
So, in the second year the salaries of Sita, Gita and Mita are respectively 8.4x, Y, 10.5x (where Y is an unknown)
We also know that Gita’s salary is the average of the salaries of the three.
This means, Gita’s salary is just the average of the other two.
∴ Y = \( \frac { 8.4 x + 10.5 x } { 2 } = 9.45 x \)
\( \frac { 9.45 x } { 7.5 x } = 1.26 \)
∴ The hike that Gita got in the second year is 26%

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The answer is '26%'

Choice A is the correct answer.