MathematicsThere were 35 students in a hostel. Due to the admission of 7 new students, the expenses of the mess were increased by Rs. 42 per day, while the average expenditure per head diminished by Rs. 1. What was the original expenditure of the mess?

There were 35 students in a hostel. Due to the admission of 7 new students, the expenses of the mess were increased by Rs. 42 per day, while the average expenditure per head diminished by Rs. 1. What was the original expenditure of the mess?


  1. A
    425
  2. B
    410
  3. C
    420
  4. D
    430 

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    Solution:

    Let the average expenditure of 35 students bex̲ After adding 7 new students, the average was decreased by 1 rupee.
    The expenses of the mess were increased by 42 rupees.
    Then, x̲=expenses of 35 students35
    Or, Expenses of 35 students = 35x̲………(i)
    After adding 7 new students, the average is
    x̲-1=Expenses of 35 students+4235+7……(ii)
    Substituting (i) in (ii) we get,
    x̲-1=35x̲+4242
    Or, 42x̲−42=35xˉ+42
    or, 7
    x̲=84
    Or, x̲=12 ----(iii)
    substituting (iii) in (i) we get
    expenses of 35 students=35x̲=35×12=420 
    Therefore, the original expenditure of the mess is 420
    Hence (3) is the correct option.
     
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