A fort has food for 150 men for 45 days. After 10 days, 25 men leave. For how many days will the remaining food last?

Given data

• Initial capacity: food for 150 men for 45 days
• After 10 days at 150 men, 25 men leave ⇒ remaining men = 125

Concept / Approach

• Use man-days: total food = (men) × (days). Food consumed is proportional to men × time.

Step-by-step calculationTotal food (man-days) = 150 × 45 = 6750Food used in first 10 days = 150 × 10 = 1500Remaining food (man-days) = 6750 − 1500 = 5250With 125 men, days left = 5250 ÷ 125 = 42

Verification42 × 125 = 5250 man-days, matching the remainder.

Common pitfalls

• Subtracting days instead of using man-days.
• Forgetting that the consumption rate changes when men leave.

Final Answer42 days