In a garrison, food was stocked for 1000 soldiers for one month (assume 30 days of rations). After 10 days, 1000 more soldiers joined (so total becomes 2000). For how many additional days will the remaining food last after the reinforcements arrive?

Introduction / Context:
Conservation of total rations (measured in soldier-days) is a common approach. We first compute the total available soldier-days, subtract what has been consumed, and then divide by the new daily consumption after reinforcements.

Given Data / Assumptions:

• Initial stock = enough for 1000 soldiers for 30 days.
• First phase = 10 days with 1000 soldiers.
• After day 10, soldiers = 2000.
• Uniform daily consumption per soldier.

Concept / Approach:
Use the soldier-day model. Total stock in soldier-days is fixed. Consumption reduces it. Remaining soldier-days divided by current soldiers gives remaining days.

Step-by-Step Solution:

Verification / Alternative check:
Total elapsed time until exhaustion = 10 (first) + 10 (remaining) = 20 days from the start. The question asks for duration after the join, hence 10 days is correct.

Why Other Options Are Wrong:
25/20/15 days conflate total-from-start with remaining or miscompute consumption. Only 10 days matches the soldier-day arithmetic post-join.

Common Pitfalls:
Not converting to soldier-days; assuming “one month” as 31; or forgetting that the question asks for the remaining duration after the reinforcements arrive.

Final Answer:
10 days