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