A fort has a stock of food that can feed 150 men for 45 days. After 10 days, 25 men leave the fort. For how many more days will the remaining food last for the men who stay?

Introduction / Context:
This is a typical work and resources problem involving food supply and varying number of people. The total amount of food is fixed, and men consume it at a constant rate. When some men leave, the daily consumption changes, which affects how long the remaining supply lasts. This is a classic chain rule scenario in aptitude tests.

Given Data / Assumptions:

• Food can feed 150 men for 45 days initially.
• All men consume food at the same constant rate.
• After 10 days, 25 men leave, so 125 men remain.
• We must find the additional number of days the remaining food will last.

Concept / Approach:
The total quantity of food can be expressed in man days, which is the product of the number of men and the number of days they can be fed. First, we calculate the total food in man days. Then we subtract what has already been consumed in the first 10 days. The remaining man days are divided by the new number of men to find how many more days the food will last.

Step-by-Step Solution:
Step 1: Total food in man days = 150 * 45 = 6750 man days.Step 2: In the first 10 days, 150 men consume 150 * 10 = 1500 man days of food.Step 3: Remaining food in man days = 6750 - 1500 = 5250 man days.Step 4: After 10 days, 25 men leave, so remaining men = 150 - 25 = 125.Step 5: Remaining days the food lasts = 5250 / 125.Step 6: 5250 / 125 = 42 days.

Verification / Alternative check:
You can check by recombining the whole period. Men consume food for 10 days with 150 men and then for 42 days with 125 men. Total consumption = 150 * 10 + 125 * 42 = 1500 + 5250 = 6750 man days, exactly the initial food supply. So the calculation is consistent.

Why Other Options Are Wrong:
36 or 38 days would give total consumption below the available 6750 man days. 45 or 54 days would mean the remaining men consume more than the stored food, which is impossible without extra supply.

Common Pitfalls:

• Forgetting to subtract the food already consumed during the first 10 days.
• Using the original 150 men instead of 125 men when computing the remaining days.
• Confusing man days with simple days and trying to compare days directly without accounting for number of men.

Final Answer:
The remaining food will last for 42 days after the 25 men leave.