Hostel rationing: Provisions for 250 men last 40 days. If 50 men leave, how long will the food last at the same daily ration?

Introduction / Context:
Again, think in person-days. A fixed stock measured in person-days divided by the new headcount gives the extended duration once some people leave while ration per person per day remains unchanged.

Given Data / Assumptions:

• Initial coverage: 250 men for 40 days.
• 50 men leave ⇒ new headcount = 200.
• Same daily ration per person.

Concept / Approach:
Total stock = 250*40 person-days. With 200 men, duration = stock / 200. No initial consumption needs subtraction because the change is immediate in the problem statement.

Step-by-Step Solution:

Verification / Alternative check:
Proportionality: duration scales inversely with headcount; reducing from 250 to 200 increases days by factor 250/200 = 1.25 ⇒ 40 * 1.25 = 50 days.

Why Other Options Are Wrong:
58, 67 overshoot; 45 undershoots; only 50 matches exact person-day math.

Common Pitfalls:
Applying partial consumption incorrectly or changing ration rate, which the question does not state.

Final Answer:
50 days