CAT 2021 Slot 3 QA Q8 Equations

Question 8 of the Quantitative Ability (QA) section, CAT 2021 Slot 3, with CAT's official answer and a worked solution.

One part of a hostel's monthly expenses is fixed, and the other part is proportional to the number of its boarders. The hostel collects ₹ 1600 per month from each boarder. When the number of boarders is 50, the profit of the hostel is ₹ 200 per boarder, and when the number of boarders is 75, the profit of the hostel is ₹ 250 per boarder. When the number of boarders is 80, the total profit of the hostel, in INR, will be
  1. A
    20800
  2. B
    20200
  3. C
    20500
  4. D
    20000

Answer: (C) 20500 Equations MCQ

Solution

  1. Expenses \(= F + vN\). At \(N = 50\): revenue \(80000\), profit \(10000\), expenses \(70000\). At \(N = 75\): revenue \(120000\), profit \(18750\), expenses \(101250\).
  2. \(25v = 31250 \Rightarrow v = 1250\); \(F = 70000 - 62500 = 7500\).
  3. At \(N = 80\): expenses \(= 7500 + 100000 = 107500\); revenue \(= 128000\); profit \(= 20500\).

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