Question

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. 20800
• B. 20200
• C. 20500
• D. 20000

Answer 1

The Correct Option is C

Let the fixed cost be ₹ F and the variable cost be ₹ V.
Since the profit per border is ₹200 when there are 50 borders
The expenses of the Hostel is,
\(F + 50(V) = 50 (1600 - 200)\)
\(F + 50(V) = 50 (1400) — (1)\)

Since the profit per border is ₹250 when there are 75 borders

The expenses of the Hostel is,
\(F + 75(V) = 75 (1600 - 250)\)
\(F + 75(V) = 75 (1350) — (2)\)
\((2) - (1)\)
\(⇒ 25(V) = 75(1350) - 50(1400)\)
\(25(V) = 25( 3(1350) - 2(1400) )\)
\(V = 3(1350) - 2(1400)\)
\(V = 4050 - 2800\)
\(V = 1250\)
\(F + 75(V) = 75 (1350)\)
\(F + 75(1250) = 75 (1350)\)
\(F = 75(100) = 7500\)

The Expenditure for 80 borders will be,
\(= F + 80(V)\)
\(= 7500 + 80(1250)\)

The revenue gathered from 80 students is,
\(= 80(1600)\)

Heelproof, the profit is,
\(= 80(1600) - (7500 + 80(1250))\)
\(= 80(1600 - 1250) - 7500\)
\(= 80(350) - 7500\)
\(= 100(8×35 - 75)\)
\(= 20500\)
Hence, when there are 80 borders the total profit is \(₹20500.\)