There were 42 students in a hostel. Due to the admission of 13 new students, 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?

1) Rs. 633.23
2) Rs. 583.3
3) Rs. 623.3
4) Rs. 632
5) None of These

• Let the original expediture of the mess per student be Rs x per day
  kTherefore,the total original expenditure of the mess per day was 42x
  When the number of students increased to 55,total expenditure beame 42x+31
  Therefore,according to the problem,
  42x+31=55(x-3)
  =>42x+31=55x-165
  =>42x-55x= -165-31
  => -13x= -196
  =>x=-196/-13=Rs.15.08
  Therefore,the orginal expenditure per student per day was Rs.15.08 and hence the daily total expenditure of the mess originally was 42*15.08=Rs.633.36
  you may,however,solve the problem in the following proess and I think it would be easier.
  Let,the total original expenditure of the hostel was Rs.x
  Therefore,according to the problem
  (x/42)-3=(x+31)/55
  =>(x-126)/42=(x+31)/55
  =>55(x-126)=42(x+31) [by cross multiplication]
  =>55x-6930=42x+1302
  =>55x-42x=1302+6930
  =>13x=8232
  =>x=8232/13=Rs633.23
  therefore,the initial expenditure of the hostel was Rs.633.23
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