CAT 2021 Slot 3 · Quant · Question 8

CAT 2021 Slot 3 previous year question on Linear Equations, with the answer and a step-by-step solution.

Linear EquationsAlgebraMultiple choiceMedium
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 ₹, will be
  1. A
    20800
  2. B
    20200
  3. C
    20500
  4. D
    20000
Pick an option, then check.
Answer & solution

Answer: Option C

Let the monthly expense for n boarders be F+kn, where F is fixed. Revenue is 1600n, so total profit is 1600n-F-kn.

At n=50 the profit is 200 per boarder, so 10000 in total: 80000-F-50k=10000, giving F+50k=70000.

At n=75 the profit is 250 per boarder, so 18750 in total: 120000-F-75k=18750, giving F+75k=101250.

Subtracting, 25k=31250, so k=1250 and then F=70000-62500=7500.

At n=80: profit =1600\times 80-7500-1250\times 80=128000-7500-100000=20500, that is ₹20500.

Note the question asks for the total profit here, not the profit per boarder.

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