A hostel has provisions for 250 students for 35 days. After 5 days, a fresh batch of 25 students was admitted to the hostel. Again after 10 days, a batch of 25 students left the hostel. How long will the remaining provisions survive? (a) 18 days (b) 19 days (c) 20 days (d) 17 days

Solution

The hostel initially has provisions for 250 students for 35 days. Let’s calculate how the provisions are affected by changes in the number of students.

Initial Provisions Consumption

For the first 5 days, 250 students consume the provisions. This consumption rate leaves provisions for 30 days for 250 students.

After 5 Days

After 5 days, 25 more students are admitted, increasing the total to 275 students. These 275 students will consume the provisions faster.

Calculation of Remaining Provisions

The total provisions can be seen as “student-days” of food. Initially, this is \(250 \times 35 = 8750\) student-days.

After 5 days of consumption by 250 students, \(250 \times 5 = 1250\) student-days of food are consumed, leaving \(8750 – 1250 = 7500\) student-days of food.

Provisions for 275 Students

For the next 10 days, there are 275 students, consuming \(275 \times 10 = 2750\) student-days of food.

After this consumption, \(7500 – 2750 = 4750\) student-days of food remain.

Adjustment for Student Departure

Following the departure of 25 students after these 10 days, 250 students remain. This is 15 days into the original 35 days.

Remaining Provisions Duration

To find out for how many more days the remaining provisions can last for 250 students:

\[
\text{Remaining days} = \frac{\text{Remaining student-days of food}}{\text{Number of students}} = \frac{4750}{250} = 19 \text{ days}
\]

Therefore, the remaining provisions will last for 19 days after the initial 5 days and the adjustments in student numbers.

The correct answer is (b) 19 days.