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.

₹1,170

Let us consider that ,

Initially Average expenditure = a

Total expenditure = 45 × a = 45a

If the number of students increases by 5, the total expenses of the mess increase by ₹30 per day

New total expenditure = ( 45a + 30 )

new average expenditure = \(\frac{45a + 30}{50}\)

According to question,

\(\frac{45a + 30}{50}\) = ( a - 2 )

45a + 30 = 50a - 100

5a = 130

1a = 26

Original total expenditure = 45 x 26 = Rs. 1170