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Hostel monthly expenses and profit calculation

CAT 2021 Slot 3 · Quantitative Ability · Hard · Profit & Loss

This is a hard Quantitative Ability question from the CAT 2021 Slot 3 paper. It tests Profit & Loss. The full answer key and a step-by-step explanation are below — try it yourself first, then reveal the solution.

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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

Explanation

Let the fixed expense be FF and variable expense per boarder be VV. Total profit P(N)=1600N−(F+VN)=(1600−V)N−FP(N) = 1600N - (F + VN) = (1600 - V)N - F.

For N=50N = 50, total profit = 50×200=1000050 \times 200 = 10000: 50(1600−V)−F=10000  ⟹  50V+F=7000050(1600 - V) - F = 10000 \implies 50V + F = 70000 --(1)

For N=75N = 75, total profit = 75×250=1875075 \times 250 = 18750: 75(1600−V)−F=18750  ⟹  75V+F=10125075(1600 - V) - F = 18750 \implies 75V + F = 101250 --(2)

Subtracting (1) from (2): 25V=31250  ⟹  V=125025V = 31250 \implies V = 1250 F=70000−50(1250)=7500F = 70000 - 50(1250) = 7500

For N=80N = 80 boarders: P(80)=80(1600−1250)−7500=80(350)−7500=28000−7500=20500P(80) = 80(1600 - 1250) - 7500 = 80(350) - 7500 = 28000 - 7500 = 20500.

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