There are 100 students in a hotel. Food provision for them is sufficient for 20 days. How long will these provisions last, if 25 more students join the hostel?

Question

Accepted Answer

To determine how long the food provisions will last after 25 more students join the hostel, we need to consider the initial situation and how the addition of students affects the consumption rate.

Initially, there are 100 students, and the food provisions are sufficient for 20 days. This means that the total amount of food is equivalent to 100 students consuming it for 20 days. We can express this as:

Total food = 100 students * 20 days = 2000 student-days of food.

When 25 more students join, the total number of students becomes 125. We need to find out how many days (let's call this 'x') the food will last for these 125 students. The total food available remains the same, so we set up the equation:

125 students * x days = 2000 student-days of food.

Solving for x:

x = 2000 student-days / 125 students = 16 days.

Therefore, the provisions will last for 16 days when 25 more students join the hostel. This supports Option 1 as the correct answer.

Now, let's explain why the other options are incorrect:

- Option 2 (20 days): This option is incorrect because it assumes that the addition of more students does not affect the duration for which the food will last. However, with more students, the food will be consumed faster, reducing the number of days the provisions will last.

- Option 3 (26 days): This option is incorrect because it suggests that the provisions will last longer with more students, which is illogical. Adding more students increases the consumption rate, thereby reducing the duration the food will last.

- Option 4 (12 days): This option is incorrect because it underestimates the duration. While the provisions will last for fewer days than initially planned, the calculation shows that they will last for 16 days, not 12.

In conclusion, the correct answer is Option 1, as the provisions will last for 16 days when 25 more students join the hostel.