CAT 2023 Slot 1 QA Q12 Ratio, Mixtures & Averages

Question 12 of the Quantitative Ability (QA) section, CAT 2023 Slot 1, with CAT's official answer and a worked solution.

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
  1. A
    26%
  2. B
    28%
  3. C
    25%
  4. D
    30%

Answer: (A) 26% Ratio, Mixtures & Averages MCQ

Solution

  1. Take salaries 5, 6, 7. After year 1: Sita \(6\), Gita \(7.5\), Mita \(8.4\).
  2. After year 2: Sita \(6\times1.4 = 8.4\), Mita \(8.4\times1.25 = 10.5\), Gita \(G\).
  3. \(G = \frac{8.4 + 10.5 + G}{3}\) gives \(2G = 18.9\), \(G = 9.45\).
  4. Hike \(= \frac{9.45}{7.5} - 1 = 0.26\), i.e. 26%.

Shortcut. Gita equals the mean of all three, so she equals the mean of the other two: \(\frac{8.4+10.5}{2} = 9.45\).

Same concept in other years

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