There were 42 students in a hostel. Due to the admission of 13 new studenets, the expenses of the mess increase by Rs. 31 per day while the average expenditure per head diminished by Rs. 3. What was the original expenditure of the mess?

Let average expenses was X per day.

Total expenses = 42X.

Now,

Total students = 42 + 13 = 55

Total expenses = 42X + 31   

Average expenses = X -3

So,

55* (X -3 ) = 42X + 31

55X - 165 = 42X + 31

55X - 42X = 31 + 165

13X = 196

X = 15.07

Original expenditure of the mess = 42X = 42 * 15.07 = Rs. 633.23