Question

In a hostel consisting of 459 students,if number of students increases by 36,the expense of mess per day increased by rs.81 while reducing the average expense per head by rs.1,find the original expenditure of mess

Answer 1

Let the original expenditure of mess = Rs. x

Original average = x/459

New number of students = 459 + 36 = 495

New expenditure = Rs. (x + 81)

New average = (x + 81)/495

The old average is greater than the new average by Rs. 1

So,

x/459 - (x + 81)/495 = 1

495x - 459x - 37179 = 227205

36x = 264384

x = 7344


Therefore, the original expenditure of mess = Rs. 7344

Answer 2

Answer: The original expenditure of mess is Rs. 16.

Step-by-step explanation:

Since we have given that

Number of students in a hostel = 459

Let the original expenditure of mess be 'x'.

Since the number of students increases by 36.

The expense of mess per day increased by Rs. 81.

The average expense per head = Rs. 1

According to question,

$495(x-1)-459x=81\\\\495x-495-459x=81\\\\36x=81+495\\\\36x=576\\\\x=\frac{576}{36}\\\\x=Rs.16$

Hence, the original expenditure of mess is Rs. 16.