In a capm, 180 students had ration for 20 days, How many students should leave the camp so that the same ration may last for 25 days ?

Answer

To solve the problem step by step, we can follow this approach:

### Step 1: Understand the Problem
We need to determine how many students should leave a camp so that the available ration lasts for 25 days instead of 20 days.

### Step 2: Calculate Total Consumption for 180 Students for 20 Days
Let the total ration be represented as \( R \). For 180 students consuming the ration for 20 days, the total consumption can be expressed as:
\[ \text{Total Consumption} = \text{Number of Students} \times \text{Days} = 180 \times 20 = 3600 \text{ student-days} \]

### Step 3: Find Consumption per Student per Day
To find the consumption per student per day, we can divide the total consumption by the number of students:
\[ \text{Consumption per Student per Day} = \frac{3600}{180} = 20 \text{ days} \]

### Step 4: Set Up the Equation for 25 Days
Let \( y \) be the number of students that will remain in the camp for 25 days. The total consumption for these students over 25 days will be:
\[ \text{Total Consumption for } y \text{ students for 25 days} = y \times 25 \]

### Step 5: Set the Total Consumption Equal to the Available Ration
Since the total consumption must equal the total ration available, we can set up the equation:
\[ y \times 25 = 3600 \]

### Step 6: Solve for \( y \)
Now, we can solve for \( y \):
\[ y = \frac{3600}{25} = 144 \]

### Step 7: Calculate the Number of Students That Should Leave
Now that we know that 144 students can stay for the ration to last 25 days, we can find out how many students need to leave:
\[ \text{Number of Students Leaving} = 180 - 144 = 36 \]

### Final Answer
Thus, **36 students should leave the camp** so that the same ration may last for 25 days.

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