Food stock after departures (man-days logic): A fort had food for 150 men for 45 days. After 10 days, 25 men left. For how many more days will the remaining food last?

Introduction / Context:This problem uses the concept of man-days: total food stock can be represented as “men × days”. After some days of consumption, the remaining stock can be reallocated among a new number of men to find how long it will last. This is a staple of work-and-time style aptitude problems.

Given Data / Assumptions:

• Total initial capacity: 150 men for 45 days ⇒ 150*45 man-days
• Consumption for first 10 days by 150 men
• After 10 days, remaining men = 150 − 25 = 125

Concept / Approach:Compute total man-days initially, subtract man-days already consumed, and then divide what remains by the new daily consumption (125 men per day) to get remaining days of supply.

Step-by-Step Solution:

Verification / Alternative check:Had nobody left, days left after 10 days would be (6750 − 1500)/150 = 35 days. Fewer men remaining (125) increases the duration: 5250/125 = 42, consistent with intuition.

Why Other Options Are Wrong:

• 39, 37, 32, 56: Do not match the computed man-day balance.

Common Pitfalls:Subtracting 10 from 45 directly without accounting for the departure of 25 men, or forgetting to convert everything into man-days before recomputing duration.

Final Answer:42