For a group of `32` students food lasts for `45` days . For how many days will the same food last for `72` students ?

Options

A. 13
B. 40
C. 20
D. 6

Answer

To solve the problem step by step, we can follow these calculations:

### Step 1: Calculate the total units of food
The total units of food can be calculated by multiplying the number of students by the number of days the food lasts:
\[ \text{Total units of food} = \text{Number of students} \times \text{Number of days} \]
For 32 students and 45 days:
\[ \text{Total units of food} = 32 \times 45 \]

### Step 2: Calculate the total units of food
Now, let's calculate:
\[ 32 \times 45 = 1440 \text{ units of food} \]

### Step 3: Determine how many days the food will last for 72 students
Now, we need to find out how many days the same amount of food (1440 units) will last for 72 students. We can set up the equation:
\[ \text{Number of days} = \frac{\text{Total units of food}}{\text{Number of students}} \]
Substituting the values we have:
\[ \text{Number of days} = \frac{1440}{72} \]

### Step 4: Calculate the number of days
Now, let's calculate:
\[ \frac{1440}{72} = 20 \text{ days} \]

### Conclusion
Therefore, the food will last for **20 days** for 72 students.

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