In a mens hostel there were initially 95 students. After 30 more students were accommodated, the average expenditure per student decreased by Rs. 5, yet the total expenditure of the hostel increased by Rs. 500. What is the total expenditure of the hostel now?

Introduction / Context:
This question combines averages with total expenditure and a change in the number of members. It is a typical hostel or club expenditure problem that appears in aptitude exams to check your understanding of how per head average and total cost change when more people join and some financial adjustment occurs. The key is to form correct algebraic equations from the given statements.

Given Data / Assumptions:

Initially there are 95 students in the hostel.
After some time 30 more students join, so the new strength becomes 125 students.
When the new students join, the average expenditure per student decreases by Rs. 5.
Despite the decrease in average, the total expenditure increases by Rs. 500.
We need to find the total expenditure of the hostel after the increase in strength, that is, for 125 students.

Concept / Approach:
Let the initial average expenditure per student be x rupees. Then the initial total expenditure is 95 * x. After 30 more students join, the new average becomes (x - 5) and the number of students is 125. Therefore, the new total expenditure is 125 * (x - 5). We are told that this new total is Rs. 500 more than the old total, so we can form a linear equation and solve for x. Finally we compute the new total expenditure using the value of x.

Step-by-Step Solution:
Step 1: Let the initial average expenditure per student be x rupees. Initial total expenditure = 95 * x. Step 2: Express the new average and new total expenditure. After 30 more students join, number of students = 95 + 30 = 125. New average expenditure per student = x - 5. New total expenditure = 125 * (x - 5). Step 3: Use the condition about the increase in total expenditure. New total expenditure = old total expenditure + 500. So, 125 * (x - 5) = 95 * x + 500. Step 4: Solve the equation for x. 125x - 625 = 95x + 500. 125x - 95x = 500 + 625. 30x = 1125, so x = 1125 / 30 = 37.5 rupees. Step 5: Compute the new average and new total expenditure. New average = x - 5 = 37.5 - 5 = 32.5 rupees. New total expenditure = 125 * 32.5 = Rs. 4062.50.

Verification / Alternative Check:
Compute the old total expenditure: 95 * 37.5 = 3562.50 rupees. The new total is 4062.50 rupees. The difference is 4062.50 - 3562.50 = 500, which matches the given increase. The new average 32.5 is exactly Rs. 5 less than the old average 37.5, which also matches the statement. Therefore, the answer is fully consistent with all conditions.

Why Other Options Are Wrong:
Option Rs. 3825 gives an incorrect new average and does not differ from the original total by Rs. 500.
Option Rs. 3937.50 also fails to produce the correct relation between old and new totals and the stated Rs. 5 drop in average.
Option Rs. 4250 makes the increase in expenditure more than Rs. 500 and therefore does not satisfy the given condition.

Common Pitfalls:
Many students confuse the change in average with direct change in total without considering the new number of students. Another common mistake is to treat 500 as the change in average instead of the total expenditure. Errors in forming the equation 125 * (x - 5) = 95 * x + 500 are also frequent, especially in handling signs when moving terms from one side to the other.

Final Answer:
The total expenditure of the hostel after accommodating the new students is Rs. 4062.50.