CAT 2025 Slot 1 QA Q11 Ratio, Mixtures & Averages

Question 11 of the Quantitative Ability (QA) section, CAT 2025 Slot 1, with CAT's official answer and a worked solution.

The ratio of the number of students in the morning shift and afternoon shift of a school was 13 : 9. After 21 students moved from the morning shift to the afternoon shift, this ratio became 19 : 14. Next, some new students joined the morning and afternoon shifts in the ratio 3 : 8 and then the ratio of the number of students in the morning shift and the afternoon shift became 5 : 4. The number of new students who joined is
  1. A
    110
  2. B
    88
  3. C
    121
  4. D
    99

Answer: (D) 99 Ratio, Mixtures & Averages MCQ

Solution

  1. Let the shifts be \(13x, 9x\). Then \(\frac{13x - 21}{9x + 21} = \frac{19}{14} \Rightarrow 182x - 294 = 171x + 399 \Rightarrow x = 63\).
  2. After the move: morning \(819 - 21 = 798\), afternoon \(567 + 21 = 588\).
  3. New students \(3y\) and \(8y\): \(\frac{798 + 3y}{588 + 8y} = \frac54 \Rightarrow 3192 + 12y = 2940 + 40y \Rightarrow y = 9\).
  4. New students \(= 11y = 99\).

Same concept in other years

See every question on Transfer between two holders changes the ratio; total stays fixed.

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