If in a hostel there is sufficient food for 30 days for 40 students, then this food will last for how many days for 60 students?

Question

Accepted Answer

To determine how long the food will last for 60 students, we can use the concept of "man-days," which is a way to calculate the total amount of food available in terms of the number of people it can feed for a certain number of days.

1. **Calculate the total man-days for the original scenario:**
   - The food is sufficient for 40 students for 30 days.
   - Total man-days = Number of students × Number of days = 40 students × 30 days = 1200 man-days.

2. **Determine how many days the food will last for 60 students:**
   - We need to find out how many days (let's call it 'x') the same amount of food (1200 man-days) will last for 60 students.
   - Using the formula: Total man-days = Number of students × Number of days
   - 1200 man-days = 60 students × x days
   - Solving for x: x = 1200 man-days / 60 students = 20 days

Therefore, the food will last for 20 days for 60 students, which corresponds to Option 1.

**Explanation for why other options are incorrect:**

- **Option 2 (24 days):** If the food lasted for 24 days for 60 students, the total man-days would be 60 students × 24 days = 1440 man-days. This exceeds the available 1200 man-days, so this option is incorrect.

- **Option 3 (18 days):** If the food lasted for 18 days for 60 students, the total man-days would be 60 students × 18 days = 1080 man-days. This is less than the available 1200 man-days, indicating that the food would last longer than 18 days, so this option is incorrect.

- **Option 4 (15 days):** If the food lasted for 15 days for 60 students, the total man-days would be 60 students × 15 days = 900 man-days. This is also less than the available 1200 man-days, indicating that the food would last longer than 15 days, so this option is incorrect.

In conclusion, the correct answer is Option 1, as the food will last for 20 days for 60 students.