Question

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. \(17\) days
• B. \(19\) days
• C. \(21\) days
• D. \(15\) days
• E. \(25\) days

Answer 1

The Correct Option is B

Concept: This is a
man-days problem:

• Total work = constant
• Work = number of students $\times$ days

Step 1: Total provisions.
\[ \text{Total} = 250 \times 35 = 8750 \text{ student-days} \]
Step 2: Consumption in first 5 days.
\[ 250 \times 5 = 1250 \] Remaining: \[ 8750 - 1250 = 7500 \]
Step 3: Next 10 days (275 students).
\[ 275 \times 10 = 2750 \] Remaining: \[ 7500 - 2750 = 4750 \]
Step 4: After 15 days, students reduce to 250.
Remaining provisions: \[ 4750 \] \[ \text{Days} = \frac{4750}{250} = 19 \]
Step 5: Option analysis.

• (A) 17: Under-calculated $\times$
• (B) 19: Correct \checkmark
• (C) 21: Incorrect $\times$
• (D) 15: Ignoring remaining food $\times$
• (E) 25: Overestimated $\times$

Conclusion:
Thus, the correct answer is
Option (B).