Students Ration Problem: Calculating Students to Leave

This problem tests understanding of inverse proportion. The total amount of ration is fixed. If the number of students decreases, the ration lasts longer, and vice versa.

Inverse Proportion Principle

Let the initial number of students be $S_1$ and the number of days the ration lasts be $D_1$. Let the final number of students be $S_2$ and the number of days the ration should last be $D_2$.

For a fixed amount of ration, the relationship is:

$ S_1 \times D_1 = S_2 \times D_2 $

Initial Conditions

• Initial students ($S_1$): 180
• Initial ration duration ($D_1$): 20 days

Desired Conditions

• Desired ration duration ($D_2$): 25 days
• Required students ($S_2$): To be calculated

Calculating Required Students ($S_2$)

Using the inverse proportion formula:

$ 180 \times 20 = S_2 \times 25 $

Solve for $S_2$:

$ S_2 = \frac{180 \times 20}{25} $

$ S_2 = \frac{3600}{25} $

$ S_2 = 144 $

This means 144 students are required for the ration to last exactly 25 days.

Calculating Students to Leave

The question asks how many students should leave. This is the difference between the initial number of students and the required number of students for the extended duration.

Number of students to leave = Initial students - Required students

Number of students to leave = $S_1 - S_2$

Number of students to leave = $180 - 144$

Number of students to leave = 36