In a fort, there are 1200 soldiers and each soldier consumes 3 kg of food per day, so the provisions last for 30 days. If some more soldiers join the fort and now each soldier consumes 2.5 kg of food per day, the same provisions last for only 25 days. How many soldiers joined the fort?

Introduction / Context:
This question involves total resources and changing consumption rates when the number of consumers increases. We are given that the total food in the fort is fixed, but both the number of soldiers and per-soldier daily consumption change. We must determine how many additional soldiers joined based on how long the provisions last under the new conditions.

Given Data / Assumptions:
• Initially, number of soldiers = 1200.
• Initial daily consumption per soldier = 3 kg.
• Provisions last for 30 days initially.
• After some new soldiers join, per soldier daily consumption becomes 2.5 kg and the provisions now last 25 days.
• Total amount of provisions in kilograms remains the same in both scenarios.

Concept / Approach:
Total provisions can be computed from the first scenario as (number of soldiers) * (daily consumption per soldier) * (number of days). In the second scenario, the same total provisions are consumed by a larger number of soldiers at a different per-soldier rate over a different period. Let the new total number of soldiers be N. Form an equation equating the total provisions from both scenarios and solve for N, then subtract the original 1200 to find the number of additional soldiers.

Step-by-Step Solution:
Step 1: Compute total provisions in the first scenario: 1200 soldiers * 3 kg/day * 30 days = 108000 kg.Step 2: Let the new total number of soldiers after joining be N.Step 3: In the second scenario, each soldier consumes 2.5 kg per day and provisions last for 25 days. So total provisions = N * 2.5 * 25.Step 4: Since total provisions are unchanged, set 108000 = N * 2.5 * 25.Step 5: Compute 2.5 * 25 = 62.5. So 108000 = 62.5N.Step 6: Solve for N: N = 108000 / 62.5 = 1728.Step 7: Additional soldiers who joined = N − 1200 = 1728 − 1200 = 528.

Verification / Alternative check:
Check the second scenario using N = 1728 soldiers. Daily total consumption = 1728 * 2.5 kg = 4320 kg per day. Over 25 days, this amounts to 4320 * 25 = 108000 kg, matching the initial total provisions. This confirms that the computed number of soldiers is consistent.

Why Other Options Are Wrong:
Options 693, 741 and 654 would give different total soldiers N that, when multiplied by 2.5 kg/day and 25 days, would not equal 108000 kg. Hence, they would contradict the conservation of total provisions.

Common Pitfalls:
Students sometimes mistakenly treat per-soldier consumption as unchanged or forget to include the change in daily consumption when forming the second scenario equation. Another error is to equate per-day totals instead of totals over the full period. Always compute total consumption (soldiers * per-soldier consumption * days) in each scenario for comparison.

Final Answer:
The number of soldiers who joined the fort is 528.