A garrison of 1000 men had provisions for 48 days. Then 600 more men arrived as reinforcement. Assuming the same daily ration per man, how many days will the provisions last now?

Introduction: This is a direct man-days allocation problem. For a fixed stock of provisions, the product of men and days is constant. An increase in the number of men reduces the duration in the same inverse proportion, assuming the per-man ration is unchanged.

Given Data / Assumptions:

• Initial men = 1000; provisions last 48 days.
• Reinforcement = 600 men; new total = 1600 men.
• Per-man daily consumption unchanged; food stock is fixed.

Concept / Approach: Total stock (man-days) = 1000 * 48. With 1600 men, new duration D = (1000 * 48) / 1600. Compute exactly to determine the number of days remaining with the larger force.

Step-by-Step Solution:

Verification / Alternative check: Ratio method: days scale by 1000/1600 = 5/8; 48 * (5/8) = 30 days, matching the exact division.

Why Other Options Are Wrong: 35, 32, 25, or 45 days do not preserve the total man-day stock given the increased headcount.

Common Pitfalls: Averaging 48 and the headcount increase or misunderstanding proportionality. Always keep men * days constant for fixed food with equal rations.

Final Answer: 30 days