Question

In a hostel of 100 students,provision was sufficient for 30 days. After one week some more students were admitted ,and the provision was consumed 3 days earlier. Find the number of students newly admitted.

Answer 1

The number of students newly admitted to the hostel is 15, which can be found by creating an equation based on the rate of consumption before and after their admission.

Step-by-step explanation:

In a hostel of 100 students where provision was sufficient for 30 days, the number of students newly admitted can be calculated by understanding the consumption rate before and after the new students arrived. Initially, the consumption for 100 students for 30 days implies that the provision would last a single student for 3000 days (100 students * 30 days).

After seven days, there are 23 days' worth of provision left for 100 students (since 30 - 7 = 23). At this point, some new students were admitted, and the provision lasted 20 days instead of 23 days, indicating an increased daily consumption rate. Hence, the provision now lasts 100 students plus the additional students for 20 days.

To find the number of new students, we set up the equation using the fact that the provision that would have lasted for 2300 student-days (100 students * 23 days) was consumed in just 20 days. Let's denote the number of new students by x. This gives us the equation (100 + x) * 20 = 2300.

We solve the equation:

• (100 + x) * 20 = 2300
• 2000 + 20x = 2300
• 20x = 300
• x = 15

Hence, the number of students newly admitted is 15.

Answer 2

Number of days for which the provisions would last initially = 30
The number of days for which the
provisions would last after new students joined = (30 - 3) days
= 27 days
So the number of students for which the provisions would last for 30 days = 100
Then
The number of students for which the provision would last for 1 day = (100/30)
= 10/3
So
The number of students for which the provision would last for 27 days = (10/3) * 27
= 90
So
The number of students that were admitted later = 100 -90
= 10
So 10 students were admitted after one week.