Given:
- Number of students in the hostel = 100
- Food provision for them is for 20 days

To find:
- How long will the provisions last if 25 more students join the group?

Solution:
Let's assume that each student consumes the same amount of food each day.

Step 1: Calculate the total amount of food available for the 100 students for 20 days.
Since there are 100 students and the food provision is for 20 days, the total amount of food available is 100 * 20 = 2000 student-days of food.

Step 2: Calculate the total number of student-days of food required.
Since there are 100 students and the food provision is for 20 days, the total number of student-days of food required is 100 * 20 = 2000 student-days of food.

Step 3: Calculate the total number of student-days of food required for the additional 25 students.
Since 25 more students join the group, the total number of student-days of food required for them is 25 * 20 = 500 student-days of food.

Step 4: Calculate the total number of student-days of food required for the entire group.
The total number of student-days of food required for the entire group, including the additional 25 students, is 2000 + 500 = 2500 student-days of food.

Step 5: Calculate the number of days the provisions will last for the entire group.
Since the total amount of food available is 2000 student-days of food and the total number of student-days of food required for the entire group is 2500 student-days of food, the provisions will last for 2000 / 2500 = 0.8 days.

Step 6: Convert the number of days to the nearest whole number.
Since the provisions cannot last for a fraction of a day, we round up the number of days to the nearest whole number. Therefore, the provisions will last for 1 day.

Conclusion:
If 25 more students join the group, the provisions will last for 1 day.