There are 45 students in a hostel. If the number of students increases by 5, the total expenses of the mess increase by ₹30 per day while the average daily expenditure per head diminishes by ₹2. Find the original total daily expenditure of the mess.

Let's assume the average daily expenditure per head was 'y' when there were 45 students in a hostel.

Total expenditure initially = $$45\times y$$ = 45y

If the number of students increases by 5, the total expenses of the mess increase by ₹30 per day while the average daily expenditure per head diminishes by ₹2.

45y+30 = (45+5)(y-2)

45y = 50(y-2)-30

45y = 50y-100-30

50y-45y = 100+30

5y = 130

y = 26

Original total daily expenditure of the mess = 45y

= $$45\times26$$

= ₹1170