Stocks for students: direct inverse proportion: A hostel has food stock for 45 days for 120 students. If 30 more students join (total 150), in how many days will the stock be exhausted, assuming equal consumption per student?

Introduction / Context:
Food stock problems are classic inverse proportion questions. If total stock is fixed and per-head daily consumption is constant, days available vary inversely with the number of consumers.

Given Data / Assumptions:

• Initial: 120 students for 45 days.
• New total: 150 students (120 + 30).
• Equal daily consumption per student; no wastage.

Concept / Approach:
Total stock S = students * days (in “student-days”). After joining, new days = S / new_students.

Step-by-Step Solution:
S = 120 * 45 = 5400 student-days.New days = 5400 / 150 = 36 days.

Verification / Alternative check:
Proportional check: Increasing students by factor 150/120 = 1.25 shrinks days by factor 1/1.25 = 0.8; 0.8 * 45 = 36 days.

Why Other Options Are Wrong:

• 38, 40, 32 do not reflect the exact inverse proportion result.

Common Pitfalls:

• Subtracting or adding days directly rather than using the product students * days constant.

Final Answer:
36