Rationing with reinforcements: A garrison of 500 persons had provisions for 27 days. After 3 days, 300 more persons arrive. For how many more days will the remaining food last?

Introduction / Context:
Food supply questions are really person-day accounting problems. Compute the total person-days available, subtract what has been consumed, then divide the remainder by the new headcount to get remaining days at the same ration level.

Given Data / Assumptions:

• Initial stock covers 500 persons for 27 days ⇒ 500*27 person-days of food.
• After 3 days at 500 persons, 300 more persons arrive.
• Ration per person per day unchanged.

Concept / Approach:
Total person-days are conserved until consumed. Remaining days = (remaining person-days) / (current headcount). Track consumption during the first 3 days, then recalculate with the new total headcount (800 persons).

Step-by-Step Solution:

Verification / Alternative check:
Sanity check: With more people, remaining days must be fewer than 27 − 3 = 24; 15 is reasonable.

Why Other Options Are Wrong:
26, 27, 28 ignore consumption and added headcount; 18 is not supported by the exact person-day computation.

Common Pitfalls:
Forgetting to subtract the 3-day consumption or dividing the original stock by the new headcount directly without accounting for the initial usage.

Final Answer:
15 days