Two thousand soldiers in a fort have food for 20 days. Some soldiers are transferred out and the same food then lasts for 25 days. How many soldiers were transferred?

Introduction:
This is another man-days conservation question. With fixed food, men × days is constant. When the duration rises from 20 to 25 days, it must be because the number of soldiers decreased proportionally. We can solve for the new headcount and then find how many left.

Given Data / Assumptions:

• Initial soldiers = 2000; initial duration = 20 days.
• After transfer, same stock lasts 25 days.
• Per-soldier daily ration unchanged.

Concept / Approach:
Total food = 2000 * 20 = 40000 soldier-days. Let remaining soldiers be S. Then S * 25 = 40000 → compute S and subtract from 2000 to get the transferred number.

Step-by-Step Solution:

Verification / Alternative check:
Check: With 1600 soldiers, duration = 40000 / 1600 = 25 days, exactly as stated.

Why Other Options Are Wrong:
450, 500, 525, 600 give remaining soldiers that do not multiply to 40000 soldier-days over 25 days.

Common Pitfalls:
Averaging 20 and 25 to guess, or thinking duration increased by 5 days implies only 5 men left; the relationship is multiplicative via man-days, not additive.

Final Answer:
400