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 $\text{INR},$ will be
- $20800$
- $20200$
- $20000$
- $20500$