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There were 46 students in a Boys hostel. Due to the admission of 8 new students the expenses of the hostel 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 hostel mess?
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There were 46 students in a Boys hostel. Due to the admission of 8 new...
Given:
- Total number of students in the Boys hostel = 46
- Number of new students admitted = 8
- Increase in expenses of the hostel mess due to the admission of new students = Rs. 42 per day
- Decrease in average expenditure per head = Rs. 1

To find:
- Original expenditure of the hostel mess

Assumptions:
- The increase in expenses is solely due to the admission of new students.
- The average expenditure per head is calculated by dividing the total expenditure by the number of students.

Solution:

Step 1: Calculate the original average expenditure per head
Let the original average expenditure per head be 'x'.

The total expenditure before the admission of new students = 46 * x (as there were 46 students)

Step 2: Calculate the new average expenditure per head
After the admission of new students, the total number of students in the hostel becomes 46 + 8 = 54.

The new average expenditure per head = (46 * x + 42) / 54

Step 3: Calculate the decrease in average expenditure per head
According to the given information, the new average expenditure per head is Rs. 1 less than the original average expenditure per head.

So, (46 * x + 42) / 54 = x - 1

Simplifying the equation, we get:
46x + 42 = 54x - 54

8x = 96
x = 12

Step 4: Calculate the original expenditure of the hostel mess
The original expenditure of the hostel mess = 46 * x = 46 * 12 = Rs. 552

Answer:
The original expenditure of the hostel mess was Rs. 552.
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There were 46 students in a Boys hostel. Due to the admission of 8 new students the expenses of the hostel 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 hostel mess?
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