In a hostel, food is enough for 50 students for 45 days. If 75 students share the same stock (no wastage, same ration), for how many days will the food last?

Introduction: Identical to other stock-sharing problems, this uses the constancy of student-days (total food). Increasing the number of students reduces the number of days inversely, with the per-student ration unchanged. The arithmetic is straightforward and exact here.

Given Data / Assumptions:

• Total food supports 50 students for 45 days.
• New student count = 75.
• Consumption per student per day remains the same.

Concept / Approach: Student-days = 50 * 45. For 75 students, new days = (50 * 45) / 75. This is the standard unitary-method structure for such problems.

Step-by-Step Solution:

Verification / Alternative check: Ratio approach: D scales by 50/75 = 2/3 → 45 * (2/3) = 30 days. Same result, faster mental math.

Why Other Options Are Wrong: 25, 28, 34, and 40 days violate the fixed student-days constraint.

Common Pitfalls: Forgetting inverse proportion: with more students and the same stock, the duration must go down.

Final Answer: 30 days