Calculating Hostel Accommodation Capacity Based on Milk Ration

This problem involves understanding the relationship between the number of students and the total consumption of milk, assuming the per capita consumption remains constant. This is a classic example of direct proportionality.

In a direct proportion, if one quantity increases, the other quantity increases at the same rate, and if one quantity decreases, the other decreases at the same rate. In this scenario, the total amount of milk consumed is directly proportional to the number of students, provided each student consumes the same amount.

Step-by-Step Solution

1. Determine Per Capita Milk Consumption

First, we need to find out how much milk one student consumes per month. This is the per capita consumption.

Given:

• Number of students initially: 90
• Total milk consumption initially: 183 litres

Per capita consumption can be calculated as:

\( \text{Per capita consumption} = \frac{\text{Total consumption}}{\text{Number of students}} \)

\( \text{Per capita consumption} = \frac{183 \text{ litres}}{90 \text{ students}} \)

\( \text{Per capita consumption} = \frac{183}{90} \text{ litres per student} \)

We can simplify this fraction later in the calculation.

2. Calculate the New Number of Students

Now we are given a new total milk ration and asked to find how many students can be accommodated with this ration, assuming the per capita consumption remains the same.

Given:

• New total milk ration: 915 litres
• Per capita consumption: \( \frac{183}{90} \) litres per student (from Step 1)

The number of students can be calculated using the formula:

\( \text{Number of students} = \frac{\text{New total ration}}{\text{Per capita consumption}} \)

\( \text{Number of students} = \frac{915 \text{ litres}}{\frac{183}{90} \text{ litres per student}} \)

To divide by a fraction, we multiply by its reciprocal:

\( \text{Number of students} = 915 \times \frac{90}{183} \)

Now, let's perform the multiplication. We can simplify by dividing 915 by 183.

\( 915 \div 183 = 5 \)

So, the calculation becomes:

\( \text{Number of students} = 5 \times 90 \)

\( \text{Number of students} = 450 \)

Therefore, with a monthly milk ration of 915 litres, 450 students can be accommodated in the hostel, assuming the per capita consumption of milk remains the same.

Summary of Calculation

Revision Table: Milk Consumption and Student Capacity

Additional Information: Direct Proportion Explained

Direct proportion is a relationship between two quantities where their ratio is constant. If quantity A is directly proportional to quantity B, we can write this as \( A \propto B \). This means that \( \frac{A}{B} = k \), where \( k \) is a constant value. If we have two different situations, denoted by subscripts 1 and 2, the relationship holds true: \( \frac{A_1}{B_1} = \frac{A_2}{B_2} \).

In this milk consumption problem:

• Quantity A is the total milk consumption.
• Quantity B is the number of students.
• The constant \( k \) is the per capita milk consumption (litres per student).

Since the per capita consumption remains the same, the ratio of total milk to the number of students is constant. We used this principle to solve the problem: \( \frac{183 \text{ litres}}{90 \text{ students}} = \frac{915 \text{ litres}}{x \text{ students}} \). Solving for \( x \) gives the new number of students.

This type of relationship is common in problems involving resources distributed among a varying number of people, where the amount per person stays fixed.