Hostel Food Provisions: Initial Scenario

Initially, there are 100 students in the hostel.

The food provisions are sufficient for these 100 students for 20 days.

Hostel Food Provisions: New Students Join

An additional 25 students join the hostel.

The new total number of students is calculated as:

$ \text{Total Students} = 100 + 25 = 125 \text{ students} $

Calculating Food Duration with More Students

This problem involves inverse proportion. If the number of students increases, the number of days the provisions last decreases proportionally.

Let $S_1$ be the initial number of students and $D_1$ be the initial number of days the provisions last.

Let $S_2$ be the final number of students and $D_2$ be the final number of days the provisions last.

The relationship is: $ S_1 \times D_1 = S_2 \times D_2 $

Solving for the New Duration

Substitute the known values into the equation:

$ 100 \text{ students} \times 20 \text{ days} = 125 \text{ students} \times D_2 $

Now, solve for $D_2$:

$ D_2 = \frac{100 \times 20}{125} $

$ D_2 = \frac{2000}{125} $

$ D_2 = 16 \text{ days} $

Therefore, the same food provisions will last for 16 days if 25 more students join the hostel.