Certainly, let's work through this question step-by-step.
### Problem Statement:
20 students in a hostel have provisions for 60 days. If 10 more students are admitted to the hostel, for how many days would the provisions be enough?
### Step-by-Step Solution:
1. Understanding the Initial Situation:
- Number of students initially = 20
- Provisions are enough for = 60 days
2. Calculate the Total Consumption:
Since the provisions are enough for 20 students for 60 days, we need to find out the total number of student-days the provisions can support.
- Total student-days = Number of students × Number of days
- Total student-days = 20 students × 60 days = 1200 student-days
3. Adding More Students:
- New total number of students = Initial students + Additional students
- New total number of students = 20 students + 10 students = 30 students
4. Finding the New Number of Days:
- Let's denote the new number of days the provisions last as [tex]\(D\)[/tex].
- The total available student-days remains the same, which is 1200 student-days.
We can set up the equation as:
[tex]\[
\text{Number of students} \times \text{Number of days} = \text{Total student-days}
\][/tex]
[tex]\[
30 \text{ students} \times D \text{ days} = 1200 \text{ student-days}
\][/tex]
5. Solving for [tex]\(D\)[/tex]:
[tex]\[
D = \frac{1200 \text{ student-days}}{30 \text{ students}}
\][/tex]
[tex]\[
D = 40 \text{ days}
\][/tex]
### Conclusion:
With the admission of 10 more students, making a total of 30 students, the provisions would be enough for 40 days.
Therefore, the answer is 40 days.
