In a school , mid day meal food is sufficient for 250 students for 33 days , if each student is given 125 g meals . 80 more students joined the school . If same of meal is given to each student , then the food will last

Options

A. 20 days
B. 40 days
C. 30 days
D. 25 days

Answer

To solve the problem, we need to determine how many days the food will last after 80 more students join the school. Let's break it down step by step.

### Step 1: Calculate the total amount of food available.
The food is sufficient for 250 students for 33 days, with each student receiving 125 grams of food.

\[ \text{Total food} = \text{Number of students} \times \text{Amount of food per student} \times \text{Number of days} \]
\[ \text{Total food} = 250 \times 125 \, \text{grams} \times 33 \, \text{days} \]
\[ \text{Total food} = 250 \times 125 \times 33 \]

### Step 2: Calculate the total food in grams.
Now, we can calculate the total food:

\[ 250 \times 125 = 31250 \, \text{grams per day} \]
\[ \text{Total food} = 31250 \times 33 = 1031250 \, \text{grams} \]

### Step 3: Determine the new total number of students.
After 80 more students join, the total number of students becomes:

\[ \text{New total students} = 250 + 80 = 330 \]

### Step 4: Set up the equation for the new scenario.
Let \( X \) be the number of days the food will last for 330 students. The total food consumed by 330 students for \( X \) days is:

\[ \text{Total food consumed} = \text{Number of students} \times \text{Amount of food per student} \times \text{Number of days} \]
\[ \text{Total food consumed} = 330 \times 125 \times X \]

### Step 5: Equate the total food available to the total food consumed.
Since the total food available remains the same, we can set up the equation:

\[ 330 \times 125 \times X = 1031250 \]

### Step 6: Solve for \( X \).
First, simplify the equation:

\[ X = \frac{1031250}{330 \times 125} \]

Now calculate \( 330 \times 125 \):

\[ 330 \times 125 = 41250 \]

Now substitute back into the equation:

\[ X = \frac{1031250}{41250} \]

Calculating \( X \):

\[ X = 25 \, \text{days} \]

### Conclusion
The food will last for **25 days** after the additional 80 students join the school.

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