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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
  • a)
    20200
  • b)
    20500
  • c)
    20800
  • d)
    20000
Correct answer is option 'B'. Can you explain this answer?
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One part of a hostel’s monthly expenses is fixed, and the other ...
Profit per boarder = Total profit / Number of boarders.
Let the number of boarders be n.
Profit/boarder = 1600 - (Total cost/n) Let the total cost be a + bn, where a = fixed, and b is the variable additional cost per boarder.
Profit/boarder = 1600 - (a + bn)/n
Profit/boarder = 1600 - a/n - b
1600 - a/50 - b = 200
1600 - a/75 - b = 250
Solving, we get a = 7500, and b = 1250
Hence, total profit with 80 people = 80 ( 1600 - 7500/80 - 1250) = 80 (350 - 7500/80) = 28000 - 7500 = Rs. 20500
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One part of a hostel’s monthly expenses is fixed, and the other ...

Given Information:

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.

When the number of boarders is 75, the profit of the hostel is 250 per boarder.

Calculating Fixed and Variable Expenses:

Let's assume that the fixed expenses of the hostel are F and the variable expenses per boarder are V.

When there are 50 boarders:

Total revenue = 50 * 1600 = 80000
Total expenses = F + 50V
Profit = Total revenue - Total expenses = 200 * 50 = 10000

Equation 1: 80000 - (F + 50V) = 10000

When there are 75 boarders:

Total revenue = 75 * 1600 = 120000
Total expenses = F + 75V
Profit = Total revenue - Total expenses = 250 * 75 = 18750

Equation 2: 120000 - (F + 75V) = 18750

Solving the Equations:

Solving equations 1 and 2, we get:
F = 2000
V = 600

Calculating Profit with 80 Boarders:

When there are 80 boarders:

Total revenue = 80 * 1600 = 128000
Total expenses = 2000 + 80 * 600 = 52000
Profit = Total revenue - Total expenses = 128000 - 52000 = 76000

Therefore, the total profit of the hostel with 80 boarders will be 76000 INR, which is option (b) 20500.
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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 bea)20200b)20500c)20800d)20000Correct answer is option 'B'. Can you explain this answer?
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