Garrison rationing with arrivals: Food is sufficient for 1000 soldiers for 1 month (assume 30 days). After 10 days, 1000 more soldiers join. For how many additional days will the remaining food last?

Introduction / Context:
Measure the stock in person-days, subtract the initial 10-day consumption, then divide the remainder by the new total headcount (after reinforcements) to compute how many more days the rations will last at the same rate.

Given Data / Assumptions:

• Total stock initially: 1000 soldiers * 30 days = 30000 person-days.
• After 10 days at 1000 soldiers, remaining stock = 30000 − 10000 = 20000 person-days.
• Then 1000 more soldiers join ⇒ total 2000 soldiers.

Concept / Approach:
Remaining duration = remaining person-days / new headcount. Keep the month as 30 days unless otherwise specified; this does not affect the proportional result because we use person-days directly.

Step-by-Step Solution:

Verification / Alternative check:
With double headcount, remaining days should be halved from 20 (if still 1000) to 10; this matches the arithmetic.

Why Other Options Are Wrong:
25, 20, 15, 12 are inconsistent with exact person-day balance after reinforcements.

Common Pitfalls:
Using calendar month length inconsistently or forgetting to subtract the first 10 days of consumption before reinforcements arrive.

Final Answer:
10 days