A fort had provision of food for 150 men for 45 days. After 10 days 25 men left the fort. The number of days for which the remaining food will last is____.

• (a) 29 1/5
• (b) 37 1/4
• (c) 42
• (d) 54

To solve this problem, we first need to determine the total amount of food available in terms of "man-days." Initially, the fort has enough food for 150 men for 45 days.

Calculating Total Food Supply

The total food supply can be calculated as:

• Total food = Number of men × Number of days
• Total food = 150 men × 45 days = 6750 man-days

Food Consumption in the First 10 Days

Next, we calculate how much food is consumed in the first 10 days:

• Food consumed = Number of men × Number of days
• Food consumed = 150 men × 10 days = 1500 man-days

Remaining Food

Now, we find out how much food is left after 10 days:

• Remaining food = Total food - Food consumed
• Remaining food = 6750 man-days - 1500 man-days = 5250 man-days

Adjusting for Men Leaving

After 10 days, 25 men leave the fort, leaving:

• Remaining men = 150 - 25 = 125 men

Calculating Remaining Days of Food

Finally, we can determine how many days the remaining food will last for the 125 men:

• Days food will last = Remaining food / Remaining men
• Days food will last = 5250 man-days / 125 men = 42 days

The number of days for which the remaining food will last is 42 days. Therefore, the correct answer is (c) 42.