Impact of Student Dropout on Expenditure in a Hostel

Understanding the financial implications of student dropout in a hostel setting is crucial for effective management. This article delves into the scenario where 10 students dropped out of a hostel with an initial number of 60 students, leading to a change in average expenditure and a reduction in total monthly expenditure. Through step-by-step calculations, this piece aims to clarify the financial adjustments required after such a change in student demographics.

Setting up the Calculation

Let's denote the following parameters for a hostel with an initial number of 60 students:

n original number of students 60 d original average expenditure per student T total expenditure for the 60 students

Given that the total expenditure can be expressed as:

T n * d 60 * d

Adjustment Post-Student Dropout

After 10 students dropped out, the number of students became 50. The new average expenditure per student is given as Rs. 25. Thus, the new total expenditure can be expressed as:

T 50 * 25

Additionally, the total expenditure decreased by Rs. 600. Therefore, we can establish the equation:

50 * 25 60d - 600

Solving for the Original Average Expenditure

Simplifying the equation:

1250 60d - 600 1850 60d d 185

The original average expenditure per student was Rs. 185.

To find the total expenditure for 60 students:

60 * 185 11100

Thus, the total amount spent on the students in a month was Rs. 11100.

Alternative Approaches and Verification

The calculations can also be verified through alternative methods. Let's denote:

x earlier expenses per student

Total expenditure 60 * x

After the dropout of 10 students, the adjustment in expenditure is as follows:

Total expenditure with 50 students 50 * (x 25) 5 * 1250 Reduction in expenditure Rs. 600

Setting up the equation:

6 - 5 * 1250 600

Simplifying:

6 - 6250 600 6 6850 x 185

The earlier average expenditure per student was again Rs. 185.

Total expenditure was: